Those fireplaces do not use 120v for the control. They use a millivolt control off a thermocouple off the gas valve. You do not need (or want) #14 wiring for this. You will regret it and I would not want to stress the terminals with such big wire. You can/should use 18/2 thermostat wire.
You can wire the two switches in parallel so that either switch will turn on the valve. Thing is both switches will have to be off for it to be off. I can't see this as a problem though.
The 120v receptacle (if it is even wired) in the unit is for an optional blower unit.