No.. It is the same grip I use for my backhand...
So the question is, what grip are you using for your BH? It really looks like you are using something closer to a FH grip on your serve. If so, using a continental will facilitate more spin on spin serves and more
pronation on flatter servers.
Could be my failing eyes, but I had a difficult time determining if you are using much forearm rotation (pronation) on your serves. As your racket moves upward from the back (scratch position), you should be leading with the blade (edge) of the racket rather than the stringbed.
The toss: It's not that your toss is too high, but your
contact point is too low (as
RT mentions above) -- this probably makes the toss look higher than it really is. It appears that your racket arm does not extend up to the ball to make contact -- the arm seems to be bent quite a bit at contact. The arm should extend so that it is comfortably straight at contact.
...
Keep your toss arm vertical for a tad longer, hold it there as you wind up.
Try to hit upwards not forwards, this should happen to some extent when you keep your toss arm vertical, and lower your serve shoulder...
I agree that the tossing arm needs to continue moving upward (to the vertical) after releasing the ball -- the trophy pose. This will do a couple of things things for your serve. Firstly, it will get your front shoulder significantly higher than your rear shoulder so that you have a better
shoulder tilt for your trophy position. Secondly, it will get your tossing hand up in the air to give you a good reference point for the toss -- it should give you a better feel for where the ball is, in space, with respect to your body.
The tossing arm should stay up there until your racket head bottoms out in the racket drop (back scratch) and is ready to start moving upward to meet the ball.
It is actually ok to drive forward (in the direction of the serve). However, you really do need to drive upward more -- upward & forward rather than just forward. The lack of arm extension is part of the problem here. Your torso also appears to lean a bit too much to the left. Try to extend your whole body upward -- lengthen the body more -- the legs extend first and then the right arm and racket extends up to the ball.