I might be able to help out from the point of view of an English native, but I'm not a director nor do I work in the film business.

1) Depending on the quality of the cut, he might say different things. If it is satisfactory: he might say "We're done here." If it is a great cut: he might say "All right! Good job guys, we're done here!" Something like this is good I think.

2) "review the cut" is probably a good term. To me, it sounds like "check the film" means that you're checking for film for physical errors/problems/breaks. "review the cut" gives more of a sense that you're reviewing the actor's performance and how it would appear to the audience.

Maybe this helps, and I'm sorry if I am wrong ^^ Anyone else have suggestions?