Momentum and Kinetic Energy (Difference and Similarity's) Physically

Question

So I have always struggled with getting the physical meaning of momentum and KE, for the longest time I just said that, 'Work and energy is just a way to look at how a force effected an object with respect to distance, while impulse and momentum were just a way to do the same but with respect to time'.
But I think, I finally got the physical meaning and just want to make sure that my understanding is right.

So momentum is the amount of motion (the movement an objects mass), While KE is the energy of that motion. When a object experiences an impulse from a force it also experiences work from that force and thus the momentum changes and so does the KE of the object. The conservation of energy is the idea that energy is never destroyed but rather converted in to other forms. While the conservation of momentum is the idea that the sum of the momenta in a system, as long as the net external force is zero, will always be the same.

So, for example in an inelastic collision, when two balls hit each other and join as one, there KE decreased, for it is converted to heat and other forms of energy, but the total sum of the balls momentum is the same before and after the collision.
In other words the amount of particles and there speeds that were moving with to the right minus the particles moving to the left is equal to the amount of particles and there speeds that were moving with to the right minus the particles moving to the left after the collision even is the overall energy of motion decreased.

Answer 1

For the most part your understanding is correct. However there was one small error:

When a object experiences an impulse from a force it also experiences work from that force and thus the momentum changes and so does the KE of the object.

It is not always the case that impulse is also accompanied by work. In other words, it is entirely possible for a force to transfer momentum without transferring energy.

Consider, for example, a person jumping upwards. The floor provides a large force upwards, and this force transfers momentum according to Newton’s 2nd law. But the floor does not move, nor does the part of the person’s foot touching the floor. Thus the work done by the floor is zero. The floor transfers momentum (impulse) but does not transfer energy (no work). Instead, the increased KE comes from the reduced chemical energy of the person jumping.