Wando - I honestly don't know what happens if the price goes up. I assume you have to pay whatever the price is whenever you make your final payment.
If the price goes up after you make your final payment then there no penalty - but there is an upgrade possible if you make a final payment and the price goes down before the penalty period begins. This is an alternative to having you cancel and rebook, or having to give you an ojboard credit.
But to answer your other question - your deposit is due the same day the penalty period starts. It varies according to whether your cruise is 1-5 days 6-8 days or 9-days+, it is 75, 90 and 90 days out.