What would happen if two galaxies collide with each other?
We actually don't have to speculate; we've observed numerous galaxies in various stages of collision and have photos to demonstrate. We also anticipate that our own galaxy will collide with the nearby Andromeda galaxy in a few billion years.
The term "collision" is a bit of a misnomer. While it's certainly possible that stars and planets would physically strike each other, what's really going on is an interaction between the two massive gravitational fields of the galaxies. This has the effect of stressing, straining and warping the structure of the galaxies, dependent upon their composition and vectors relative to one another.
Generally speaking, the result (after many, many years) would be a single composite galaxy, probably surrounded by small satellite galaxies consisting of "chunks" flung off during the collision process.
If two galaxies would collide each other there would be constant collisions between the planets, stars, asteroids etc. It would be a war of the cosmos.
But, I think there would be no collisions further because the universe is expanding at a great speed and this is how all the galaxies are moving apart.