Shulchan Aruch and Rama, Yore Dea 115:2, indicate that cheese made by a non-Jew can't be eaten unless a Jew saw it being made. Kraft, a national brand, now has some Ⓤ-certified reduced-fat mozzarella cheese. Is a Jew present constantly, or is there some reason he doesn't have to be?
You can ask the OU to confirm, but yes, they have a Jew present constantly when the cheese is being made.
They may have some days where the cheese is not Kosher and they have arrangements to have that sold as non-Kosher.
Yes, that is expensive. Next to meat, it is the most expensive form of Kosher certification.