The amp size of a wire is determined by its gauge, not the number of wires. An 8-gauge wire is typically rated for around 40-60 amps, depending on the type and insulation of the wire.
Use 8 gauge wire.
The amp rating of NM (Non-Metallic) wire varies depending on the gauge of the wire. For example, a 14-gauge NM wire typically has an amp rating of 15 amps, while a 12-gauge NM wire has an amp rating of 20 amps. It is important to consult local building codes and regulations to determine the appropriate wire gauge and amp rating for specific applications.
# 3 gauge
Normally it is a 20 amp using AWG 12/2 gauge wire. But it really depends on what size wire is on that circuit. If it is white AWG 14 gauge then use a 15 amp breaker. If it is yellow AWG 12 gauge then use a 20 amp breaker.
wire gauge is used to determine the size of the wire to be installed based on the amperage draw of whatever is being hooked up on the receiving end. ie 14 gauge is for a 15 amp circuit, 12 gauge is for a 20 amp circuit, 10 gauge 30 amp etc. to get specific amp draw ratings on a particular gauge of wire look at a current National Electric code book or ugly book.
2 or 4
You should use a 4 guage wire. There is a handy chart located at http://www.the12volt.com/info/recwirsz.asp which lists the proper wire size for differing wattages.
You listed no gauge wire. This is the required breakers.14 gauge - 15 amp12 gauge - 20 amp10 gauge - 30 amp8 gauge - 40 amp
30 amp breaker with #10 gauge copper wire
For a 20 amp circuit, a 12-gauge copper ground wire is typically recommended. This wire size can safely handle the current and provide proper grounding for the circuit.
14 gauge will handle it with a 15 amp breaker. If you use 12 gauge use a 20 amp breaker.