Can you leave and re-enter? If yes, do you get some kind of stamp? What about readmittance for parking?

Keep receipts and get stamp

Repay for parking, but they wi give a stamp so you can come back with no charge

Yes they stamp your hand. I don't think you can do that for parking

I believe you get a stamp to get back in the park but for the parking I think you have to repay

Yes you can leave and return. Not sure about parking.