According to the paper I linked to, Proxima’s period is 591,000 years. It’s near apastron (furthest point in its orbit from the other two). As for other stars passing close, see Scholz’s Star.
This of course would apply to whatever galaxy we decide is closest but not part of the Milky Way. These kinds of questions are always poorly defined, since as Chronos pointed out, it doesn’t say what happens to the light outside our galaxy that’s already on the way here.
Maybe, although my understanding is that we aren’t actually in orbit around Andromeda. The two galaxies have not actually circled each other (the universe isn’t old enough for that to have happened). We’re just falling towards each other.
Consider what is part of the Solar System. Perhaps the best definition is “the Sun and everything in orbit around it”. Can you think of a better definition (with the appropriate changes) for what is part of the galaxy?
We certainly can’t say that our Galaxy and the Andromeda galaxy are on a collision course. They might be, but we can’t tell. All we can actually tell is that we’re currently getting closer to each other. But then, when you’re on the freeway and look at cars on the other side of the median, they’re getting closer to you, too. That doesn’t mean that you’re going to collide.
Has that changed since 2012? I thought thesethreepapers showed that Andromeda’s transverse motion was small enough that the collision was inevitable. (Wikipedia, Nature)