It's going to take a whopper of a wire to run a 20 amps 650 feet. I'd feel more comfortable if a journeyman electrician would come by to access my answer. But, my calculations show it would take 4 AWG wire to do it. If you want you could run two 7 AWG wires in parallel.
This is a voltage drop question. To answer this question you need to state a voltage. If this is not a commercial or industrial three phase question, the voltage will be considered at 120 and 240 volts.
A #4 copper conductor or a #2 aluminium will limit the voltage drop to 3% or less when supplying 100 amps for 300 feet on a 240 volt system.
A #1 copper conductor or a 2/0 aluminium will limit the voltage drop to 3% or less when supplying 20 amps for 650 feet on a 120 volt system.
12 gauge underground wire or if you think you will ever add any devices to this circuit use 10 gauge.
No. The wire size is dependent on the circuit protection. If the circuit uses a 20 amp breaker you need to run 12 AWG wire on all devices connected to that circuit.
Depends on the size of the circuit which you did not list.
Depends on how many amps it pulls and the size of the wire in the circuit.
Assuming you are working with 120v, you need #4 AWG copper conductors.
Cannot answer this question. Will need to know the voltage and amperage of the circuit. Also need to know the application i.e. is it a lighting circuit or a motor circuit?
AWG 10 guage.
8 AWG copper.
AWG 2/0 copper wire.
8 ga
12 gauge underground wire or if you think you will ever add any devices to this circuit use 10 gauge.
Depends on the size of the circuit which you did not list.
No. The wire size is dependent on the circuit protection. If the circuit uses a 20 amp breaker you need to run 12 AWG wire on all devices connected to that circuit.
Number 10 thnn copper wire.
If this question is asking about voltage drop, to size a wire, a voltage is needed.
Need more information. Wattage of bulb, voltage of bulb, voltage of battery and wire size of the circuit.
The smaller the wire size used in a circuit limits the amount of current that is allow to be flow through that circuit.