You book all those things under "My Cruise Plans" on the
DCL site. Go to the very bottom of the cruise plan page and there you will find the buttons to click on spa tx,
castaway cay & Nassau excursions. They seemed to have plenty of everything except Palo's & Cabanas. Plenty of Remy ressies too. brunch/high tea are only only on certain days. which makes them very limited.
But of course you can always check when you board. You pick the time you want to board when you fill out your online check in. don't forget to do that.