I have a question about ship overlapping before the movement phase is over...

Say I have Ship A has a move that places it in an overlapped position with ship B but ship B moves AFTER ship A. After Ship B moves, Ship A would no longer be overlapping with it.

How is that resolved? Do you stop Ship A's movement, resolved Ship B's movement and return to Ship A afterwards, OR does Ship A stop where it touches Ship B (and loses its action) and then ship B moves on to its new position afterwards?

Finally...does the answer change if the pilots both have the same score?

The fact that ship B hasn't moved yet doesn't matter. The only thing that matters is where it is currently. So you'd follow the second option you list. It moves back until it's touching B and lose it action. The move B after.

Pilot Skill doesn't change anything in this case. Once you activate A you have to finish moving A. The only thing PS would do in this case is if you notice A would overlap B and you control both ships you could move B first.

This is why having the same PS skill can be beneficial. If they were both PS2, you could move ship B out of the way before A would bump with it.

Or, deliberately bump ship A knowing it might save him from hitting an obstacle or enemy ship, and so letting him shoot still.

Remember too that if A overlaps B and B subsequently moves, the two ships CAN attack each other. I've run into a lot of people who think not being able to attack stays in effect even if one of the ships subsequently moves away.

Remember too that if A overlaps B and B subsequently moves, the two ships CAN attack each other. I've run into a lot of people who think not being able to attack stays in effect even if one of the ships subsequently moves away.

Except in the case where B may get bumped back to its starting position which is still in contact with A.

To add another point: bumping only means you skip your "Perform Action" step in the Activation Phase. Free actions granted by other abilities post-bump (Squad Leader, for example) can still be taken, even if you are overlapping a ship still.