If you lose ball speed when you feel like you are relaxing, then either you were really putting a lot of force into your swing before, or you are actually holding back the ball by slowing it down (which is still muscling the ball). What speed is your ball going when you feel relaxed?
Gripping and a broken wrist are two different, independent things. If you break your wrist you will most likely need to grip the ball, but if you keep your wrist firm or slightly cupped you will be able to keep the ball on your hand without gripping.
If the ball is still falling off your hand with a firm wrist then your span might be wrong, or your thumb hole could be too big, or it could have too much reverse pitch.
Your actual body position and finished position look pretty good, but there are a few things I can see to work on. You don't have much of a backswing which to me says you are probably stopping the ball in your backswing, probably because as was pointed out you start the ball on your 3rd step instead of your 2nd step. It also looks like you might be pulling the ball forward based on how quick your follow through gets up to your shoulder and bounces back down. Also, at the release you are both on top of and on the outside of the ball, which works well for throwing a straight ball but not well if you are trying to get rotation on it so it will hook.
I think the reason the ball goes at the angle it does is because you are standing pretty far to the left and I'm guessing you are aiming at about the 2nd arrow, which is causing you to pull the ball across your body a little bit to hit that target. Also, being on the outside of the ball might be causing it to kind of fall of to the right as soon as it comes off your hand, as opposed to keeping your hand behind the ball and projecting it straighter down the lane.
If you can get a sideview of you bowling that would help us to see some aspects of your game that are hard to see from behind.
USBC Bronze Coach