Hand position depends on which foot forward. Its how you would hold a baseball bat. If you are Left Foot Forward (front foot) with the handle horizontal in front of you, your left hand palm would be down (over) and your right hand palm up (under). If you are Right foot forward it would be opposite. This position is static on both sides.
The purpose of releasing the handle really becomes important as the line is shortened. You need to reach and extend out to get around the buoy at short line lengths. But it also helps with balance and rhythm in the turn.
Ideally you should keep both hands on and hold the handle in close to your body after you cross the wakes and go into your pre-turn. At 15off you want to hold the handle until you get to buoy width then release the outside hand and hold it near your outside hip. The inside hand you will extend toward the boat, maybe slightly forward. As you come out of the turn you want to try and ski back into the handle and grab it then.