1) Yes. From the rules:
Levitate: ...When Levitating a Rock, move the Rock simultaneous with your moving Sorcerer. (The Levitated Rock follows the same movement path as the Sorcerer.) ... e.g. The Sorcerer moves one square forward. Then also move the chosen Rock one square forward.
2) No. Again from the rules:
...(* All moves are mandatory.) ... - Play then alternates turns between players, providing three moves* each turn. During each turn you MUST perform your moves (steps) with any of your three pieces. Each piece has its own unique way of acting. (Spread your obligatory amount of moves among your pieces as desired.)