Game behavior can be tied so closely to quirky hardware behavior that I doubt such a tool would be simple to create. You’d have to verify that your code produces the same hardware state. And different (ie more efficient) code almost by definition produces a different hardware state than the original code. Thus changing the game.

Because byte-for-byte identical output is far easier to measure than trying to test for functional equivalence.

This is also partly a preservation activity so (as best we can create it) identical code generating identical output is a big part of the point.

It's usually just the first sweep to make sure everything is understood and documented before you start to make mods.

No. Halting problem.