How long can I have the water heater off and the water supply to the water heater off? I can't make repairs right away but I have a serious leak in the hot water faucet in the bathtub so I want to cut off the hot water.

As long as you like jturner. No need to be concerned.. heck , people go on vacation and shut down for months!!

I saw from earlier post that you have a gas heater. So just shut gas supply into heater via the gas shutoff... OR could also shut off at the gas valve/thermostat to heater... just turn knob on top to off. Let us know if you need more info.

You could also set the gas valve to pilot... that way you will not need to relight the pilot when you restart heater.

Yes, as long as the heater is off, you can have the water turned off you are OK, If it is going to be months, you may want to drain it, but I assume you are talking about days or weeks at most.