Re your first question, see my answer to how can galaxies collide if everything moving outwards. All galaxies have relative motions superimposed on their motion due to the Hubble expansion. This is because the distribution of matter was uneven follwing the end of inflation and the uneven distribution resulted in uneven gravitational attraction and hence uneven motion.
Actually this is quite a good thing, because if the motion of all particles in the universe had been exactly uniform we'd still have a thin soup of atoms instead of stars and galaxies, and I wouldn't be around to answer this question. The aggregation of matter into clumps and the relative velocities of the galaxies stem from the same source.
Re your second question, there is lots of info and videos on modelling galaxy collisions. Googling will find you many hours worth of browsing. In a galaxy collision it's likely that no stars will collide because stars are so much smaller than galaxies, so at least in the outer reaches of the galaxy solar systems shouldn't be greatly affected. Near the core there may be stellar approaches close enough to disrupt planetary orbits and/or trigger cascades of comet's from the Oort cloud. I don't know of any quantitative work on this.