Even with the rule that a piece can't return to a square it's just come from, it can just make an endless square, which is just a slightly longer version of the side-to-side repetition.

If a 3 attacks and loses it could be a 4 or 5 that it attacked. But even so, that's part of the strategy - why not add more and more helpful features to make the game easier until we might as well let the game play itself?

If you want to keep track, make notes for yourself.

No, saved boards only apply and can only be used for the variant they were set up for.

Yes, it seems to do that sometimes...i'm not quite sure why or when... :-)