We have set the status for the room to provisional. When the admin confirms the booking, the status should be automatically set from provisional to booked.

The confirmation status and approval status are two independent settings. It is possible to have a booking that is approved that is still tentative. For example the administrator may approve a booking but the meeting might not yet happen for some reason.

Is it possible to have different mail notifications when request for approval and New booking .

Not at the moment, but I will look at that as a feature request.