Can physical therapists diagnose and if so what?

Who Can't? Most certainly physical therapists can and do make or at least verify diagnosis daily. I have relied on the expertise of physical therapists to confirm or add to my initial diagnosis on hundreds of patients. If you are asking if they can legally initiate an opinion as a diagnosis, That would better be answered by the states licensing act for physical therapists.
Yes depends. In some states, physical therapist can see you for evaluation and treatment without a referral from a physician. This would mainly be related to muscle skeletal issues.