14 gauge copper
10 gauge will work fine.
12 gauge wire is sufficient. Any larger is fine, but superfluous.
10 kw or 10,000 watts divided by 240 volts equals 41.6666 amps. 8 gauge is borderline so you will need 6 gauge wire to be safe.
The link below shows a typical usage and a chart
Yes 220 & 240 are considered the same.
Yes <<>> In North America, a three wire 120/240 volt system uses a neutral wire. For 240 volts two "hot" wires are used with no neutral.
A #10 wire with an insulation factor of 60,75 and 90 degrees C is rated at 30 amps.
A #6 copper wire with an insulation rating of 90 degree C is rated at 65 amps.