A #8 wire with an insulation rating of 75 or 90 degrees C is rated at 45 amps.
At the service entrance you will need AWG 1/0 gauge.
A #3 copper wire with an insulation factor 90 degree C is rated at 105 amps.
You would need to use a #12 copper conductor to continuously draw 14 amps at 120 volts.
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.
15 amps
A # 14 copper conductor will be fine to carry 8 amps at 120 volts. This size conductor is rated at 15 amps.
AWG # 10.
30 amps.
Ohm's Law states Volts = Amps x Resistance. You would need to apply 600 volts across 3 ohm load to have 200 Amps flow in circuit. Not sure what you are really asking and why you mentioned 2 gauge.
14 gauge wire is for 15 amp circuits. At 220 volts that would be enough for 2.4 kw.At 120 volts it would need 12 gauge wire which is rated for 20 amps.
140 AMPS
A #14 wire will do the job.