The ampacity of a # 10 copper wire with an insulation factor of 90 degrees C is 30 amps. All wire voltage ratings usually drop into two categories 300 volts and 600 volts. Home wiring drops into the 300 volt range and commercial, industrial, drops into the 600 volt range.
A #8, 90 degree C rated copper wire is rated at 45 amps, a #6 90 degree rated aluminium wire is rated at 55 amps.
25sqmm copper or 35 sqmm Al
A #6 copper conductor will limit the voltage drop to 2% or less when supplying 50 amps for 80 feet on a 240 volt system.
5 amps
You can't. The 120 volt GFCI is probably just a 2-wire (hot, neutral and ground) You would have to run a new 3-wire (2 hots, neutral and ground). The two hots are how you get the 240 volts (120+120=240). Also you must make sure the wire is gauged properly. #10 wire for 30 amps, #12 wire for 20 amps, etc.
At 120 Volts you would draw about 42 amps. At 240 Volts it would be about 21 amps. For 120 Volts you would need 6 AWG and for 240 Volts you would need 10 AWG.
A 2/0 copper conductor will limit the voltage drop to 3% or less when supplying 125 amps for 230 feet on a 240 volt system.
A #6 copper conductor will limit the voltage drop to 2% or less when supplying 50 amps for 80 feet on a 240 volt system.
10 mm2 cross section should be sufficient (#6 wire?)
5 amps
A #6 aluminum conductor will limit the voltage drop to 3% or less when supplying 20 amps for 200 feet on a 240 volt system.
10 gauge will work fine.
A #10 copper conductor will limit the voltage drop to 3% or less when supplying 21 amps for 150 feet on a 240 volt system.
A #14 wire will do the job.
30 amps.
10 gauge
At the service entrance you will need AWG 1/0 gauge.
You can't. The 120 volt GFCI is probably just a 2-wire (hot, neutral and ground) You would have to run a new 3-wire (2 hots, neutral and ground). The two hots are how you get the 240 volts (120+120=240). Also you must make sure the wire is gauged properly. #10 wire for 30 amps, #12 wire for 20 amps, etc.
AWG # 10.