In the US of A, it's supposed to be black.
No, not a good idea. You have to use a 347 volt ballast.
For wiring in the USA the Neutral conductor is required to be white or gray by the National Electrical Code.
yes
black
AWG # 10 wire on 30 amp circuit.
Yes, you can always have heavier wire than code requires.
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.
Only if the cable going to your well pump is a three wire. The third wire could carry the neutral and you will have 120 volts from either 240 leg to the neutral.
Because the white wire on a 120 volt circuit is the neutral wire that is connected to the silver screw on outlets and switches. It is connected to the neutral bar in the service panel.
Where there is a red wire involved that usually indicates some type of special switching arrangement or more likely a 240 Volt circuit. In this case there will be 240 volts across the red and black and they will both be hot. Normally for 120 Volts the black is hot, the white is common and the bare wire is ground.
Yes, but it will not work.
14 AWG wire normally supplies 15 amps. Watts = Volts x Amps x Power Factor. Power Factor has a maximum value of one. If you have a 120 volt circuit that would be 15 x 120 = 1800 watts or 1.8 KW. For a 240 volt circuit 3.6 KW.