[drsshivaprakash (OP)]

We know that the universe is expanding. What I would like to know is whether the galaxies are expanding by themselves (like in situation 1 blown up)? (please refer to the images below).
If the galaxies are not expanding by themselves but, only moving apart as the universe is expanding then what is the boundary of our galaxy (marked M).
How would we ever know if we have reached the boundary of our galaxy?
Would the spreading thin of the galaxy mean that whatever is holding our galaxy together ("dark energy/dark matter") is weakening - because it is allowing the galaxy to spread or if it was being held in place to the same size with the expansion of the universe are we postulating that there is dark material being created out of nothing (is that even possible)?

[PmbPhy]

We know that the universe is expanding. What I would like to know is whether the galaxies are expanding by themselves (like in situation 1 blown up)? (please refer to the images below).
If the galaxies are not expanding by themselves but, only moving apart as the universe is expanding then what is the boundary of our galaxy (marked M).
How would we ever know if we have reached the boundary of our galaxy?
Would the spreading thin of the galaxy mean that whatever is holding our galaxy together ("dark energy/dark matter") is weakening - because it is allowing the galaxy to spread or if it was being held in place to the same size with the expansion of the universe are we postulating that there is dark material being created out of nothing (is that even possible)?

No. Galaxies are not expanding. The forces which hold them together are significantly greater than that which is required to overcome expansion of the universe. I myself am expanding but that's due to eating too much.

[evan_au]

what is the boundary of our galaxy?

That is a question that I am sure astronomers will debate for a long time, before drawing an arbitrary line
- Like the arbitrary Kármán line that says "Space starts at an altitude of 100km", even though Earth's atmosphere extends far beyond that, getting thinner and thinner the higher you go.

Stars get thinner and thinner, the farther you travel from the center of our galaxy
- There are some "dwarf galaxies" that are orbiting our Milky Way galaxy
- This list shows 38 of them closer than Andromeda galaxy
https://en.wikipedia.org/wiki/List_of_nearest_galaxies
- These dwarf galaxies passing through our galaxy would have left a faint trail of stars behind them, and would have tugged a faint halo of stars out of our galaxy
- Traditional telescopes can't see these individual stars, and can't even detect these low-luminosity patches of light, since they are fainter than the night sky, even on a good night in a good location
- But some new types of survey telescopes are better at detecting low-luminosity patches of stars, when looking away from the galactic disk, and may succeed in extending the fuzzy boundary of our galaxy
- but they won't extend the boundary very much in the galactic plane, since there are too many stars and patches of dust in the galactic plane, which will hide a faint outer band of stars
See: https://en.wikipedia.org/wiki/Low_Surface_Brightness_galaxy

When Andromeda galaxy collides with our galaxy (in about 5 billion years), this messy collision will spray stars in all directions, many of which will end up orbiting as a faint halo around the new, combined galaxy.
- We probably have a faint halo of stars from previous collisions