I'm pretty sure the finishing cheese is pecorino Romano. Both me and my partner thought it had the telltale Romano "funk". And Dom buys all of his stock (tomatoes, cherry tomatoes, flour, etc) from one single distributor. (I can't recall who, but it was fairly easy to figure out with your google machine)
Also, the Asian kid is not his son, just a long term employee/apprentice. His son is the small guy (mid 20s?) that stays in the back. Otherwise he has daughters that work but I don't know how regularly. When Dom retires, it will survive based on the daughters' desire to keep it going.