Use 8 gauge wire.
# 3 gauge
AWG # 10 wire on 30 amp circuit.
Depends on the size of the circuit which you did not list.
The ground wire in a two or three conductor #12 cable is a #14 bare ground wire.
No !
I would use AWG # 4 copper.
Yes, no problem at all going to a larger ampacity of wire. Larger size wire yes, smaller size wire no.
If it is a 110 volt light it can safely run on a 20 amp circuit with AWG # 12 wire.
You use the correct size breaker depending on the size wire in the circuit. If the circuit is wired with AWG #12 wire use a 20 amp breaker. If it is wired with AWG #14 wire then use a 15 amp breaker.
Answer for USA, Canada and countries running a 60 Hz supply service.240 volt two wire circuits loads do not need a neutral to operate. A three wire 240 volt circuit that needs a neutral, will have a neutral the same size as the current carrying conductors. In this case a #10.
4 copper
NEC states that all GFCI's require a 20 amp circuit, the wire size for a 20 amp circuit is 12 gauge.