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The NEC calls for these circuits to have Arc Fault Circuit Interruptor - AFCI - whether the building official will allow regular breakers on the existing circuits varies widely by jurisdiction. The building official has the final word.
It has been my experience over the years working in many jurisdictions that most inspectors are willing to work with you as long as you are up front with them.
I recommend giving them a call or speaking to him/her when you apply for the permit.
Hi, I'm Mike G
Arc fault breakers are a good idea but not required on existing circuits unless they are extended over 6 ft. If the wiring method you mentioned is actually a BX cable, the sheath and foil within are the ground. If so, grounded receptacles may be installed and ground provided with a jumper wire to the outlet box. If the method is a flex cable, a GFCI breaker would be the solution.