[Europan Ocean (OP)]

Proxima Centauri b orbits a red dwarf star which is the nearest star to the Earth, Proxima Centauri. Since it is a red dwarf, does this mean it was once a red giant and it may have engulfed the planet in flames? I think I asked before, and it was said that it was never a red giant. So it may still have air and water, or does a red giant add air and gas to a planet?

[Halc]

Proxima Centauri b orbits a red dwarf star

Proxima Centauri B is a planet orbiting the red dwarf  Proxima Centauri, yes. Proxima Centauri is the red dwarf and it orbits the larger two stars which have within 10% either way of the mass of our own sun, and so neither is a red dwarf.

Since it is a red dwarf, does this mean it was once a red giant and it may have engulfed the planet in flames?

No star in the system has yet to reach the red giant phase.  The dwarf is too small to do something like that. 

I think I asked before, and it was said that it was never a red giant. So it may still have air and water, or does a red giant add air and gas to a planet?

It is in the habitable zone.  It's composition is not easily determined.  Some atmosphere is possible.  Water is too, but not likely.  There are only two planets in our solar system with more than traces of liquid water on them.

[Europan Ocean (OP)]

https://en.wikipedia.org/wiki/Alpha_Centauri#Confirmed_planets

This article mentions the three stars and a known planet.

[Janus]

Proxima Centauri b orbits a red dwarf star which is the nearest star to the Earth, Proxima Centauri. Since it is a red dwarf, does this mean it was once a red giant and it may have engulfed the planet in flames? I think I asked before, and it was said that it was never a red giant. So it may still have air and water, or does a red giant add air and gas to a planet?

Red dwarfs are low mass stars that are still in their early stages of their lifespans.  A star like Proxima, which is roughly 12% the mass of our Sun, will continue to burn pretty much the same way as it is now for a long time to come (Unilke larger stars like our own, the hydrogen and helium in the star is constantly circulated, and the helium doesn't build up in the core. It is this build up in the core that will eventual lead to our Sun expanding into a red giant.)   
The life spans of red dwarfs are so long that the universe isn't old enough for one to have reached the end its main life cycle.
White dwarfs are what moderate mass red giants end up shrinking down to. 

Proxima b is not likely to have any air or water.  Even though it is in what is called the "habitable zone", this only describes the distance to be to have the right temp to have liquid water.  However, since Proxima is such a small star, it is only about 1/600 as bright as the Sun. This means the planet has to be really close to it in order to get enough heat.  But being that close in subjects it to very strong solar winds which would tend to strip away any atmosphere.

[Europan Ocean (OP)]

If Proxima b is bigger than the earth, it may have a bigger magnetosphere, could this trap water?

We can compare Mercury and Venus, the latter is close to the Sun and has a very thick atmosphere. Smaller than the Earth, yet inside maybe more Iron?

[Janus]

If Proxima b is bigger than the earth, it may have a bigger magnetosphere, could this trap water?

We can compare Mercury and Venus, the latter is close to the Sun and has a very thick atmosphere. Smaller than the Earth, yet inside maybe more Iron?

The size of a planet has nothing to do with its magnetic field, which is generated by its spinning core.  One of the issues with orbiting so close to the star is that the planet is going to be tidally locked so that it rotation and orbit have the same period. Since Proxima b takes about 11 days to orbit, it would also take 11 days to rotate. The slower rotation doesn't bode well for generating a strong field. 
It is estimated that  Proxima loses mass to solar wind at a rate about 1/5 of that of our Sun, but Proxima b is only about 1/20 of the distance from its star than the Earth is from the Sun. This ends up with the Solar wind being more than 80 times stronger for Proxima b than it is for the Earth. 

While this does not completely rule out Proxima b from having a viable biosphere, it does but it at very long odds.