In June, the lovely host at Giovanni’s made all of my reservations for me while I had lunch on boarding day. I had the unlimited dining package. It was great! I always eat at off times and was able to get every reservation I wanted. In the past, I had concierges take care of it, but I wasn’t in a suite that trip.
As for shows, you don’t need a reservation for any shows. Just get there early for the ice skating shows, as others have said they do fill up quickly.