What are pre collisions and post collisions in forces and momentum? What are pre collision and post collision exactly? I assume it is before collision and after collision. I can not find an answer on google.
 A: Yes, you are right. 
Pre collision is the state of a particle or a System of particles before the collision happens. And post collision the states after collision.
A: Welcome to Physics StackExchange! 
Yes, it is exactly that. Because collisions are impulsive, the effects of a collision cannot be handled by the usual implementation of Newton's second law relating force to mass and acceleration. 
So instead, the conservation laws are written down, relating the momenta (and kinetic energies) before and after the collision to the impulse (force integrated over the very short time of the collision). Usually, in order to completely solve the dynamical problem, an extra condition needs to be imposed: for example, that the colliding surfaces are smooth, and hence the impulse acts perpendicular to them, at the point of impact.
A: Collisions take place in 2 phases, the deformation phase, during which the velocity of the faster particle decreases, and the velocity of the slower particle decreases, till they become equal to the velocity of the COM, and the reformation phase, during which the initially slower particle increases in speed, beyond that of the COM. These 2 are the ones I presume you're referring to. 
The forces here are impulsive, which makes it impossible to write down force equations, so we use impulse momentum equations;
$$ J= \int F(t)dt $$
$$ J_{deformation} = \int_{0}^{t_0} F(t)dt$$
$$ J_{reformation} = \int_{t_0}^{t_f} F(t)dt$$
Where F is the impulsive force acting on the bodies.
You'll realise that $J_{deformation}$ is nothing but $ ∆\vec p_1$ (the change in momentum of particle (1))
And $J_{deformation}=∆\vec p_2$
This allows us to do all sorts of calculations. Do note that at any given point, the impulses acting on each particle is equal and opposite (ie an impulse J acting on one particle, is -J on the other).
