[Captain Foresight (OP)]

Considering the universe is constantly expanding, why do nebula and stars contained therein have what would appear to be the same shape as viewed by the” ancient Greeks”

[Kryptid]

A few thousand years is pretty much nothing compared to stellar scales of time. Space and stars are enormous compared to human scales. Spatial expansion also does not occur to an appreciable extent inside the Milky Way.

[Colin2B]

Considering the universe is constantly expanding, why do nebula and stars contained therein have what would appear to be the same shape as viewed by the” ancient Greeks”

The star constellations do not have the same shape now as in previous era. It’s not to do with expansion but relative drift between different systems. There are some astronomy apps that will show you the changes over time, but don’t expect dramatic shifts.

[evan_au]

You have to admit - the constellations do not look much like their names, at first glance.

I heard that some researchers had extrapolated stellar proper motions backward in time to see what the constellations would have looked like thousands of years ago. They came up with some date that they thought the familiar Ancient Greek constellations looked "most like" their name. From this they deduced a date when these constellations may have been originally named.
- I've not heard of the same thing being done for Australian Aboriginal constellations, which are apparently more about galactic dust clouds, and it would be much harder to measure a proper motion (compared to an individual star)..

Of course there is another explanation that I heard, about some Ancient Greek astronomers spending the night outside, with a very large amphora of ouzo...

[Bored chemist]

Of course there is another explanation that I heard, about some Ancient Greek astronomers spending the night outside, with a very large amphora of ouzo

I'm fairly sure that the names pre-date the discovery of distillation.
So they must have been drinking something else.
When was retsina invented?

[Janus]

Considering the universe is constantly expanding, why do nebula and stars contained therein have what would appear to be the same shape as viewed by the” ancient Greeks”

Gravitational attraction overcomes the expansion until fairly large scales. Anything smaller than a galaxy cluster is bound together by gravity and resists expansion.  So when they say the universe is expanding, they mean overall, but not locally. Galaxy clusters move apart, but the galaxies within each cluster don't. 
When you get down to smaller scales, like our local group of galaxies, you can even have galaxies on (slow motion) collision courses.  The Andromeda galaxy, for example, will(possibly*) collide with ours in 4.5 billion years. This means that in the last 10,000 years it has only decreased its distance to us by 0.0002222... %  Not exactly something noticeable by even the keenest observer.

*We don't have an accurate enough measure of its exact direction of travel to say for sure if it will be a collision or a very near miss.

[SeanB]

Retsina was probably invented by the first person to make wine, using a pine wood vessel to hold the crushed grapes to ferment, likely originally by accident in collecting lots of grapes to make raising, and them finding the crushed ones at the base, and leaving the liquid for a few days, then trying the liquid.

[CatherineMaguire]

It is a well known fact that stars that we see don't exist anymore, the distance of light is blamed in the consequence that we see them now

[evan_au]

It is a well known fact that stars that we see don't exist anymore

It is a well known expectation that most of the stars we see with our eyes do still exist.
- There are a few exceptions, such as a few stars that are thought to be nearing the end of their lives, and displaying some instability. They are very bright, so we see them from far away, and it is possible that they have already gone supernova.
- But most of the stars we can see have life expectancies far in excess of the light-travel time.

[CatherineMaguire]

It is a well known fact that stars that we see don't exist anymore

It is a well known expectation that most of the stars we see with our eyes do still exist.

Ok, I agree, but there are more theories and, anyway, the most spread away is that we
see
just the stars' light which don't exist anymore

[Origin]

just the stars' light which don't exist anymore

Not really.  For example light (photons) from the sun that don't hit anything will essentially exist for ever, they will just be red shifted from the expansion of space.

[evan_au]

a few stars that are thought to be nearing the end of their lives

Here is a "Top 10" list of stars thought to be ready to "pop their top", along with a short bio of each...
For many of them, light takes over 1,000 years to reach us,
https://naturenoon.com/next-star-supernova/

Here is a more technical list (with a lot less description):
https://en.wikipedia.org/wiki/List_of_supernova_candidates

Astronomers expect 1 supernova in our galaxy about every 50 years, but historical records suggest that we only can see a naked-eye supernova about every 400 years (theories for the discrepancy vary...).
Overall, out of the roughly 7,000 individual stars visible in the night sky, probably all of them will still be visible next year.

[Deecart]

It is a well known fact that stars that we see don't exist anymore, the distance of light is blamed in the consequence that we see them now

At some point you are right.
If you consider that what you name "stars" are in fact galaxies or clusters of galaxies, it is true that, accordingly to the big bang therory and the expansion that come with it, already 97% of galaxies are actualy, from our point of view, unreachable.
Because 97% of all the galaxies inside the observable universe are recessing faster then the speed of light.
At some point, i think that we can say that physicaly speaking they do not exists for us any more.

But many "bright points" in the sky are also stars, real stars, because we are in our galaxy and we speak then of the stars of our galaxy.

There are 100 billions of visible galaxies (reachable or not) and 100 billions of stars in our galaxy (or 400 billions but this is around this).
So let say half of the "bright points" are stars and half of them are galaxies ( galaxies and same for stars)

[Halc]

The OP asked about 'visible' stars in a context of constellations and such, implying it is objects visible without aid of instruments not available to the 'ancient Greeks'.

Hence the list is limited to about 2500 stars (7000 according to @evan_au who apparently lives in a unlikely dark place), the vast majority of which likely still exist today.
The list of potential stars that are exceptions were all particularly nearby and bright things, suggesting that there's a far more boring list of similar candidates that are just barely visible due to their far greater distance. But this greater distance also increases the window in which it can cease to exist.  We see very few dim stars like our own, and most of them are fairly large bright distant stars.

We see at least one galaxy (I can still spot it here without aid despite the light pollution), but no individual stars in it are visible. The galaxy is assuredly still there, so I don't think it counts as something that has self-destructed in the time it took for the light to get here.

If you consider that what you name "stars" are in fact galaxies or clusters of galaxies, it is true that, accordingly to the big bang therory and the expansion that come with it, already 97% of galaxies are actualy, from our point of view, unreachable.
Because 97% of all the galaxies inside the observable universe are recessing faster then the speed of light.

Having a recession speed greater than light isn't what prevents us from getting to most of them. We see them, and they see us, so clearly something is 'getting to them'.  What prevents us from getting to them is being beyond their event horizon, and while that event horizon and the distance where things have a recession rate (measured in cosmological coordinates) greater than c is close to it, it is inside, and we can theoretically reach something currently receding at a rate greater than c. Just not much faster.

In the absence of acceleration of expansion, there would be no point in the universe that is unreachable regardless of recession rate. But there is acceleration, and that means that our local group of galaxies will never reach another group. Our current neighbors are all we will ever have.

At some point, i think that we can say that physicaly speaking they do not exists for us any more.

If you can see it, it physically exists (at least with a measurement definition of 'exists', and I don't know of a better definition), and over time, new objects come into the visible universe. They cannot leave it by definition, so over time, more and more stuff exists to us, despite all of it eventually fading to red to the point of undetectability.  There is a limit beyond which we will never see even in infinite time, and currently about 60% of that is within our visible universe, and the other 40% will move in over time. Everything else will never 'exist' in any meaningful way.

There are 100 billions of visible galaxies (reachable or not) and 100 billions of stars in our galaxy (or 400 billions but this is around this).
So let say half of the "bright points" are stars and half of them are galaxies ( galaxies and same for stars)

I think, given a good telescope, that there are far more galaxies visible than local (in our galaxy) stars. The deep field shots you see are all galaxies and no stars. The shots looking into our own galaxy find it impossible to see through the dust and other material obscuring the view. The vast majority of stars are not visible, but the galaxies are unless they happen to lie on the same plane where all the obscured stars are. I am unsure of the percentage of the deep sky that is available for unobscured viewing.

News: Earlier this year they broke the record for most distant object (called SD1), with a redshift of ~13¼, breaking the old record of about 11. The JWST did not get credit for this find. SD1 is young, small and bright, but I suspect it very much still exists (certainly as part of something bigger just like us) today.

[Deecart]

What i mean is :

Fisrt point =>

Although single stars from other galaxies can’t be seen with ours eye alone, some galaxies and nebula can be. For example, the Andromeda galaxy is a collection of over 1 trillion stars approximately 2.5 million light-years away. It can be seen as a fuzzy oval in the night sky, although you need a clear night in a rural area to see it.

https://www.spaceanswers.com/solar-system/could-a-human-survive-on-the-surface-of-mercury/

You can easily do confusion between stars and galaxies.

Today, when talking about stars and deep sky objects being ‘in’ a given constellation, astronomers mean to say that they lie within the defined boundaries of the constellation. Constellations themselves are not real, since the stars and deep sky objects (nebulae, galaxies, clusters) belonging to them lie at very different distances from Earth and only appear close to one another because they lie in the same line of sight when seen from Earth.

Since the stars and other visible objects are located at different distances, this also means that we are seeing them as they were at very different points in the past and not as they appear now. Antares in Scorpius, for instance, lies about 550 light years from Earth. We are therefore seeing it as it appeared some 550 years ago. The Trifid Nebula in Sagittarius is approximately 4,100 light years distant, so the image we are seeing is 4,100 years old. Galaxies lie at even greater distances. The famous Antennae Galaxies in Corvus are located some 45 million light years from Earth. This makes the images of the colliding pair 45 million years old.

https://www.constellation-guide.com/what-is-a-constellation/

[evan_au]

The deep field shots you see are all galaxies and no stars

There are a few nearby stars in any significant area of the sky.

The JWST Deep Field released last week was said to cover a fraction of the sky equivalent to a grain of sand held at arm's length.
- But even in this small fraction of the sky there were some individual stars, recognizable by the 6 radiating "spokes" - these are diffraction effects from the hexagonal mirrors, and the three supports for the prime focus mirror.
- This is different from galaxies, which tend to be fainter and fuzzier. Because they are fainter, the diffraction effects aren't so noticeable.
- Stars in Hubble images have "cross hairs" from the optical support structures inside Hubble, which are at right-angles.
- Looking closer at the JWST image, the stars also have some less prominent horizontal lines; I assume that these are from some other part of the optical path which has horizontal and vertical supports (like Hubble)

Webb_First_Deep_Field_NASA.png (1222.29 kB . 1462x896 - viewed 2431 times)

[JesWade21]

We use parallax for nearby stars. This is the effect of the relative shifting of star positions as the earth revolves around the sun over the course of a year. You can observe parallax by observing how objects appear to shift positions when one eye is closed and the other is open, and vice versa. It becomes more complicated as the number of stars increases. I'm on my phone right now, so I don't want to make any complicated claims without references, but it frequently involves analysing the light of distant stars (further than 400 light years). The colour of a star is directly related to its brightness. We can tell how bright a star should be by its colour.

[Origin]

The colour of a star is directly related to its brightness.

I don't believe this is correct.  The color of a star is directly related to it's temperature not brightness.  For instance a red dwarf and a red giant with the same color will have the same surface temperature but the red giant will be much brighter.

[evan_au]

We use parallax for nearby stars... (for) distant stars (further than 400 light years)

The Gaia spacecraft has taken parallax measurement  to a whole new level, with unparalleled precision in plotting star positions on the sky.

In conjunction with ground-based Doppler measurements, it has measured the 3-D position and velocity of a billion stars in our own galaxy, and even stars in the the Large Magellenic Cloud dwarf galaxy (150,000 light-years away).
https://en.wikipedia.org/wiki/Gaia_(spacecraft)

[Bored chemist]

The colour of a star is directly related to its brightness.

I don't believe this is correct.  The color of a star is directly related to it's temperature not brightness.  For instance a red dwarf and a red giant with the same color will have the same surface temperature but the red giant will be much brighter.

The apparent brightness is related to temperature, distance and size.
The colour is related to temperature.
It might be possible to disentangle them.