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# 6 copper wire.
This is a voltage drop question. A voltage must be stated to answer this question.
A #6 copper wire with an insulation factor of 75 or 90 degree C is rated at 65 amps.
For that distance I would run AWG # 3 copper and install a sub-panel.
here is a wire gauge calculator which will answer your questions http://www.powerstream.com/Wire_Size.htm
AWG 4 copper.
A 3/0 copper conductor will limit the voltage drop to 3% or less when supplying 200 amps for 200 feet on a 240 volt system.
Depends on the size of the sub-panel in that garage. If you are installing a 60 amp sub-panel 400 feet away from the main service panel then use AWG # 4.
That can't be answered until you state the voltage.
Assuming its copper. Number #3 or #2 is fine
It depends on the supply voltage because at that distance the size of the wire is calculated on the volt-drop which is 5% of the supply voltage, or 3% in some countries. The allowable resistance equals the volt-drop divided by the current, then you can use wire tables to find the wire size, remembering that a supply needs 2 wires which are in series so that their resistances add. <<>> To answer this question a voltage value has to be stated. This is due to the higher the voltage the lower the current on a specific load. The lower the current, the smaller the wire size can be.
This is a voltage drop question. To receive an answer to this question the voltage of the service must be stated.