You will not need a park reservation for the park the party is in.
You will need a park reservation for “a” park that day, and a park hopper ticket or AP, if the party is in a different park from the party.
It would be the same as a dining reservation. You can hop to a park to use a dining reservation.
No, the dining or dessert party reservation would not guarantee you entrance to the park, if by some reason hopping was not allowed that day. But since hopping has been available at every park, every day since it restarted, and capacity is only increasing, I do not anticipate it ever being a problem. The only days I would be sure to book the party in the same park I had a reservation for would be between Christmas and New Years, and that has to do with total park capacity, not hopping.