I am finishing a basement bedroom. I have a circuit for the garage, with a circuit with "basement lights". The existing garage circuit feeds an outlet in the basement mechanical room. May I feed the future bedroom of this garage circuit, and convert the "basement lights" circuit into the new basement bathroom circuit?
You should run a seperate circuit from your electrical panel to the new basement bedroom circuit. It should be wired to an arc-fault circuit breaker in your panel. The unfinished garage and mechanical room most likely have concrete floors which is considered a wet location. These outlets should be ground-fault circuits. You can install 2 gfci outlets for most convience. Or one gfci at the first box, and feed out from the load terminals to the next box.
All electricity in the bedroom should be fed from the arc-fault breaker, including the required smoke detectors inside and outside of the bedroom.