Can we leave the park and come back to the same park during the day

Yes, I believe so.

Make sure you keep the receipt for your parking. If you leave and come back and don't have your parking receipt you will have to pay again. Parking is $25, unless you want preferred which is $50.

Yes

Yes at least the same kingdom, if you pay for the hopper option you can return to any kingdom

Yes, the standard ticket allows access to one park per day, with in/out privileges. The park hopper option allows you to hit multiple parks on the same day.

Greater please