Hi @selghazaly 
Welcome to the Canvas Community. That's a good question, and it never occurred to me in the past to see if this was possible, though I suspected not. I could not tell for certainty from the documentation, so I finally just checked myself on a test class and then logging in as an observer in the class. (I have admin rights, so I could login as a student.) The answer is NO. Observers cannot book appointments via Scheduler. In fact, even if they are observing a specific student, the Observer not see that other student's appointment, either...which somewhat surprised me. But the bottom line is that Observers do have not Scheduler access.
I hope this helps, Sherihan.
