It could be a suspension problem if you are compressing it too far as you hit the face, which would kick you higher in the air.
However I used to have the same problem and could not figure out why--I had a couple embarrassing moments as I would try frantically to get my feet back on the pegs before I landed and landed on the rear brake pedal or shifter.
GRIP THE TANK HARD WITH YOUR KNEES. This is what I was forgetting to do--as I launched, I would release my grip on the tank without knowing it. But if I concentrate on keeping my knees in tight to the tank, my feet stay where they're supposed to. No more problem.
As for your nose diving problem, even though you're on the gas, try blipping the throttle a bit as you leave the lip of the jump. This will keep your front end higher as you sail. You can also rev in the air to raise the front if you're airborne long enough. Similarly, if you are flying through the air and feel too nose-high, you can hit the rear brake to drop it (pull the clutch in so you don't kill the motor--that's bad news in mid air!). I have never tried these technniques as I am seldom airborne long enough to think about it and when I am, all I can think about is "OMG I'm going to die!" But blipping the throttle as you launch and revving in the air should help you land easier.
Give it a try!