Visible Stars in Andromeda Galaxy So when I look at images taken of Andromeda, I see a lot of individual stars. 


Image by André van der Hoeven

It seems to me that the actual individual stars that far away would be too small to resolve, even with a big scope like the Hubble. So, I have to assume that these points of light that I see are either a) stars in our own galaxy, or b) other distant galaxies, like we would see in the Hubble Deep Field:



So I decided to think a little about this ... so I chose what I presume is big, bright star: R136a1. This one is about 30 times the size of the sun, and 8.7 million times as bright. We can barely see this thing with a telescope, and it's 163,000 light years away. Andromeda however, is 2.5 million LY away, over 15 times as far, which would make the light ... what ... 15 squared... 235 times as faint?

I have to imagine that the glow from the galaxy comes from the scattering and reflecting of all the collective starlight inside the galaxy off the dust and gas and whatnot contained therein, and that the actual individual stars would be kind of like individual droplets of water in a cloud. Almost kind of like when you can briefly see the form of a cloud when lightning flashes inside it at night (even though the light really isn't coming from the droplets)

Am I even close to correct in thinking this?

Thanks
You are right that most of the dots of light that you see in the at image of Andromeda are stars in our galaxy that happen to be on the same alignment.

However we can resolve stars in the Andromeda galaxy. (Here I am understanding "resolve" means "to see as individuals and not just a haze")

https://www.spacetelescope.org/images/heic1502a/zoomable/

Even without the Hubble telescope, individual stars had been identified in the Andromeda galaxy, and (since the brightness of some of these stars can be determined) the distance was calculated. This was also done by Hubble, but by the man, not the telescope.  He found that the Andromeda galaxy was not part of the Milky Way, but much further away.

Hubble's photograph from 1923 can be compared to a modern skysurvey image.

The light in the image that you show is the combined light from billions of stars. They are too dim to be seen at the resolution of your image, but combine to make what looks like a shining cloud.  Just like a real cloud is made of lots of dots of water that are too small to see.

There are background galaxies. Some can be seen on the high resolution view I link above. One surprising thing is how small the area of the sky in the Hubble Deep field image is. It would be only a few pixels across on the scale of the image you have of the Andromeda galaxy.

You could expect that many galaxies to be in every few pixels, but too dim to be seen in the image of Andromeda.