You have several problems involving the same basic principles:
Momentum is the product of mass and velocity. It has the same units as Impulse, which is commonly described as a force acting through a distance. Impulse can cause a change in momentum, and vice-versa.
When objects interact---momentum is always conserved
Consider a simple example: An object with mass M1 is moving with velocity V1. It hits another (stationary) object with mass of M2. The combined mass is now larger, so the velocity will be lower.
The momentum equation:
M1*V1 + M2*V2 = (M1+M2)*V(new)
Keep in mind that momentum is a vector quantity---meaning that the direction of motion must be taken into account. Example: 2 identical objects travelling at the same speed---one going due north, and other due east. After the collision, their combined speed will be sum of the original speed, and the direction will be northeast.
Recognize the differences between momentum and energy. While momentum is always conserved, energy is only conserved if the collision is totally elastic---meaning that all of the the energy absorbed in the collision is recovered as kinetic energy----as opposed to being converted to heat, sound, or some other form.
If all this is not "clicking" for you, spend some time with the various online resources such as Wikipedia or Khan Academy.