can paltalk administrators open and close rooms when they like?

Answer 1

Yes,

If you have a account that is paid account you can create your own room and add others to help admin your room. You are the room owner/admin. You and any other admin with your code can then open the room. Closing the room is the same thing.

Now Paltalk also have Paid Admins that work for them to visit rooms and check for violations and they have the ability to close a room and block users, if the violation is sever enough they can ban users. (you will not know who the pal adminastration people are)

Answer 2

yes