No, you do not have to sign-up for the rock-climbing in advance (or at least not until the day you are interested in doing it). They have frequent open-sessions and you just sign-up that day in available time slot.
As for the Ice Show, watch for the announcement in your CruiseCompass (the daily newsletter). They will distribute tickets for the shows (same show performed 4 times) at a specified time and place on a first-come, first-served basis.
Hope that helps-