I just bought a new car like most of you know. The dealer gave me a bottle of this carecraft wax/sealer. It took the yellow splatters off with some heavy rubbing. Is this safe for my clear coat? Is it safe to use the liquid turtle wax as a cleaner and rub fairly hard with it?

You shouldn't rub hard at all on new paint
http://www.topoftheline.com/tolae/

if its a sealer you can rub as hard as you want , you could use a polisher or a buffer to apply and remove it as long as you know how. By hand it should be able to take hard rubbing with sealer after bieng painted 30 days. Just find out if that product can be applied that way , should say on the bottle.