12 AWG. You can run several hundred feet.
12 gauge underground wire or if you think you will ever add any devices to this circuit use 10 gauge.
A #8 copper wire with an insulation factor of 75 or 90 degrees C is rated at 45 amps.
It depends upon the length of the circuit, but for 50 feet or less a 10 gauge wire should be fine. A short length (15 feet), you could use 12 gauge. If you double the length to 100 feet, you should use 8 gauge. A rule of thumb is to drop down a gauge for every length that is doubled. There are wire size charts available on the internet. Some can be conservative such as recommending #8 for 50 ft or less at 30 amps. It is better to be conservative than to run too much amperage on a smaller wire that can cause a fire. As a general rule, 12ga wire can be used in house circuits for 20amps or less. 16ga wire can be used for 15 amps or less such as lighting circuits. That is considering lengths of less than 100 feet.
14-3 Is the standard wire use for residental smoke detectors.
4 gauge
This is a voltage drop question. To answer this question a voltage must be stated.
This is a voltage drop question. To answer this question an amperage is needed.
8 ga
12 AWG. You can run several hundred feet.
here is a wire gauge calculator which will answer your questions http://www.powerstream.com/Wire_Size.htm
12 gauge underground wire or if you think you will ever add any devices to this circuit use 10 gauge.
This is a voltage drop question. To answer this question a voltage must be stated.
A #3 copper conductor will do the job.
No, you can never mix wire sizes in a circuit.
yes
first off. it has to be UF type wire, and is usually 12 gauge or 10, depending what you are using it for.