But the thing that boggles my mind is that despite the appearance of catastrophe on a titanic scale, the distances involved means it is highly unlikely individual stars will even come close, let alone collide.
Come to think of it... isn't that the Andromeda Galaxy just over the horizon???
As you say the stars may not even come close to each other but the gravitational forces at work would be a bit uncomfortable for any poor planet I suspect.
The effects on any planets orbiting the stars of two colliding galaxies is the same as it is for the stars. Unless they come really close to one another, the planets are unaffected.