Yes to both, with some restrictions. I've used a tripod to video parades and shows such as Tarzan, MGM Stunt Show, Off Kilter, British Invasion etc. and that's allowed. There are some rides, ToT, R'n'Rollercoaster and others where video taping is forbidden/discouraged, but with a small camera and a little discretion it can be done. In addition I've taped POTC, BTMRR, SplMtn, Safari and others too numerous to mention.
Some unsolicited advice if this is truely once in a lifetime, capture some film but don't let it dominate the trip to the extent that all you actually remember later on is the act of filming. Experience the place.
Bill From PA