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.
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.
Assuming you are working with 120v, you need #4 AWG copper conductors.
The wire size depends on how much current it will conduct.
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?
The recommended wire size for a 30A circuit is typically 10-gauge wire.
The recommended wire size for a 40A circuit is typically 8-gauge wire.
The recommended wire size for a 60A circuit is typically 6 AWG (American Wire Gauge) for copper wire.
The recommended wire size for a 220v electrical circuit is typically 10-gauge wire.
The recommended wire size for a 240V electrical circuit is typically 10-gauge wire.
The recommended wire size for a 30 amp circuit is typically 10 gauge wire.
The recommended wire size for a 60 amp circuit is typically 6-gauge wire.
The appropriate wire size for a 20 amp circuit is typically 12-gauge wire.
For a 25 amp circuit, the appropriate wire size is typically 10 gauge wire.
The appropriate wire size for a 30 amp circuit is typically 10 gauge wire.
The appropriate wire size for a 50 amp circuit is typically 6-gauge wire.