I have a problem with understanding the nature of collisions and their outcomes. From my understanding, I come to think that when a mass collides with another, both of them should always have equal velocities post-collision. For example, when a mass moving at v1, m1, collides with a mass at rest, m2, their velocity after collision should always be m1v1 / m1 + m2. My justification for this is that once they reach the said velocity, they are not colliding anymore, they are moving along together, they have zero kinetic energy, relative to each other. I don't understand how is it that there are cases in which one mass loses it momentum completely to the other mass and other cases in which m1 may even rebound: how can any change in momentum still occur after they have equal velocities?
I also have problems understanding what governs the magnitude of impulse at collision: is it possible to predict the magnitude of the force and the duration of which the applied force will last? It seems, from all the problems on impulse that I have seen, it's impossible because the problems always have to give some information about the momentum pre and post collision, never only pre collision.
What am I failing to understand?