if I purchase a ticket for Sunday Dec. 30 (Parts one and two) does the ticket include both performances

You will have two tickets. One for each performance

Each part has its own ticket. If you purchased both one and two for the same day, then you should see both parts. Check your tickets carefully. Having the digital copy on your phone is a great backup.

There is a restaurant guide at the Cursed Child website. We went to a diner and had no trouble getting seated. Juniors or Westway Diner are bith giid choices. We had plenty of time and didn't feel rushed. You don't want to be late for Part 2.

Yes and you'll have a break in between to go get dinner. But its times square so you will want to make a reservation wherever you intend to eat. We made ours for 5pm when we went last week.

Each part is a different ticket that you have to buy. If you bought both tickets at once, then you should be able to see both parts.

Yes. You should have one for the mat. Then the second say. 7.30pm