1. Can you take a moon for a good and then when you cash it in, opt not to pay and not to take anything?
Yes. You might not be able to pay for the good, but you can still grab a moon just to rush the end of the turn.
2. When moving a prince to the palace/watchman/virgins/priests/plaza, only THAT player gets to use the space, whereas the other places on the board allows everyone to use it?
Correct. (Though not "everyone" can use the other places--only those with Incas there.)