A #14 wire will do the job.
Watts = Amps x Volts. Amps = Watts/Voltage. Amps = 2500/apply voltage here.
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
AWG # 10.
If we assume that the inverter is used in your car on 12 Volts DC and you are creating 120 VAC; and the 2500 watts refers to the AC side of inverter then for a resistive load Amps = Watts / Volts = 2500/120.
Use this formula Amps = Watts/Volts.
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.
5 amps
Generally 40 amps continuous or 50 amps surge is safe.