If the unit moves on the floor but does not leak onto the floor then you probably have a newer plumbing system in your house which has plastic waste and vent pipe in that case the closet flange was not screwed down to the plywood floor prior to setting the toilet bowl on it and tightening the closet bolts that hold the bowl down. Remember the toilet bowl bolts to the closet flange and if the closet flange was not properly installed then you will have problems with the toilet moving or rocking on the floor. As far as how tight to tighten the closet bolts that is hard to explain just snug it up evenly thats all I can tell you it comes with expierience.

Leaks at the floor or the tank where it meets the base behind the seat?

Generally tight enough to sinch it so as not to leak.

If the whole unit moves on the floor the wax ring may need to be replaced. If the tank leaks be sure the bolts are tightened evenly with new gaskets sealing them inside the tank. Tighten the nuts evenly until it stops moving freely and the leak should stop.