To answer this question a voltage needs to be stated. The formula needed to find the amperage is I = W/E. Amps = Watts/Voltage. Once the amperage is found, the proper size conductor to handle that current can be established. Without knowing the amperage on 400 watts a good guess would be a #14 wire. This wire size is good up to 1440 watts at 120 volts.
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This is a voltage drop question. To answer this question a voltage has to be stated. Amps = Watts/Volts. Without this value the question can not be answered.
You need to look at the regulations that apply in your country. If in doubt, use a neutral wire of the same size as the live wire or wires.
It will power two 400 watt lamps.
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.
The key parameter in sizing wire is the current requirement. Once you know that you can look up value in a wire gauge table. The length of the run is important for longer runs because of the resistance of the wire itself. Aluminum wire requires a larger diameter than copper for the same current. Once you calculate the wire size you can then size the conduit.
500mcm 37 strand copper wire = 1.544lbs/ft.