Rare. I have never heard of that happening. It is possible that there might already be a crack in a tooth that is further exposed by a dental cleaning. Dental cleaning is good for your and harmless.
Deep cleanings. Deep cleanings do not cause tooth fractures.
Usually not. If a tooth is compromised, any intervention may be problematic. For regular hygiene visits or for scaling and root planing, teeth fractures or restoration failure is rare. If you feel an area is a problem or an existing restoration is loose, tell your dentist or hygienst prior to the procedure.