The answer to your second question is that prior to Saturday, Diaz had last pitched on the prior Monday. He had four days off, and needed the work to stay sharp. That's the dilemma with closers. Sometimes you have to use them just to give them the work - and then they get more work than they can handle.
Re your first question, the Mets are going to give Familia a long leash. They just are. They have too much invested in him not to. Let's see how he's doing a month from now. He's going to get at least that.