leaving the tee in the ground is not a bad thing at all
You should be hitting the ball "on the up" with a driver...it all depends on how you are doing it.
If you are scouping (breaking down of impact wrist) then you are basically lobbing the ball into the air.

As was said, if you chop down on the ball it will pop up and go nowhere also.

Try some tape on the face (or talc on the ball, etc) to see where on the face you are hitting the ball.

Try a much slower swing and concentrate on hitting the ball with your hands before the clubhead, just to ingrain the correct feeling.

10.5 shouldnt be giving you any height issues.
How far do you hit the rest of your clubs?
Another question, is there much difference between how far you hit your fairway woods from the Tee versus the fairway?