Yes, you can just go and watch, have no idea what it would cost for lessons.
As for the ice skating, they offer open skating, plus they put on an amazing ice show a few days into the cruise. You'll have to pick up the comp. tickets for it, since they can't hold that many people in there at a time, so the days/times are divided up. Be sure to catch that, its really worth seeing.
You can have a personal session for one hour that will cost you $83 or a group session -- which offers training , tips and techniques as well a vigorous workout on the punching bags and other boxing equipment -- for $10.
SS Norway (12 times) '85 - '97; Radiance OS 06/01; Island Princess 11/04, Grand Princess 11/04/05, Golden Princess 7/21/06, Golden Princess 2/24/07, Explorer of the Seas 12/23/07, Island Princess 11/15/08