Can a dentist who is a carrier of mrsa safely treat a patient that has risk of infectious endocarditis from certain dental procedures due to mitral valve repair with annuloplasty ring that takes 3gms amoxcillin for tooth extraction ?

Yes: At least in the US all dentists use universal precautions that protect themselves & the patient from chance exposure to germs of any sort. The idea of MRSA carrier is something of a myth. MRSA is readily found in the environment in general & accounts for 70% of outpatient boils treated by docs. You are exposed to it every day several time whether you are aware or not.