Yes you can, they won't be having any effect on the root now...

Yes, but I would wait a while before trimming off the leaves. The cold weather will cause it to transfer its sugars from the leaves, down to the roots, making the parsnips sweeter & more delicious. Wait for 1 or 2 frosts to pass.

Depends if Torontopete gets frosts of course, he doesn't say where he is in the UK.