Well done, you've got this more-or-less correct. Just one or two fairly minor points:
Originally Posted by NathanBUK
I agree with your answers to (a) and (b).
For part (c), I think you should say:
The distance between P and Q would be unchanged, because we are assuming that the particle is influenced only by gravity.(which I suspect is what you meant, but didn't actually say so).
I agree with your answer to (d).
For (e) the magnitude of the velocity at Q is at an angle of below the horizontal. You have just given the magnitude of its horizontal component.