why we do the things we do to calculate collision response between 2d rigid bodies

Hey looking at this page which describes how to calculate collisions between any two polygons, I have a few questions on why the author takes some of the steps he does. He thoroughly shows how to calculate the results, but not why he does some things.

First, if you crtl F "we call this the relative velocity" for context, I want to know why it is the relative velocity needs to be calculated; It seems we could just calculate the change in the momentum between the two Points of collision on each body, and translate that back to the CM? And is all the mass of the body pushing against the other body even though it's hitting the other body at an angle?

Second if you ctrl F "relative normal velocity must be negative", Does this mean body A must always be to the left? Is there other ways to do this if it's to the right?

What happens if the collision point on body B is not a side, but a corner point with no perpendicular line?

Third if you ctrl F "convert the change in angular momentum to a change in angular velocity", How is it that the same impulse or change in momentum is used for both angular and linear calculations? They are two very different momentums aren't they?

Thanks for any help!

First: "The change in the momentum between the two Points of collision on each body"? I can't figure out what that means. But the method I think you mean would be equivalent to the "relative velocity" approach, just a little more complicated.

Second: No, there's nothing in that equation that pertains to "left" or "right". And if the point of collision on B is a corner, then it's safe to say that the point of collision on A is a side; whichever body is hit on a side, call it "B".

Third: Nope, a linear momentum times a radius gives you an angular momentum. Physics is just cool that way.