A creature occupying an illegal space will automatically be shunted to the closest legal space at the end of its movement, so they should simply be pushed back. No similar rule exists for objects, so it should revert to the DM's adjudication.
This is not specified in the book, and it's always been a contentious topic. Expect table variation.
Only if it's delivered through a claw or bite attack.
Usually this will require holding the charge.Those hit by a ghoul’s bite or claw attack must succeed on a DC 12 Fortitude save or be paralyzed for 1d4+1 rounds.