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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.
A 10 mm cable is most commonly used for a 500 KVA transformer, 240 volt, 3 phrase. The size of the wire that is used in a transformer is based on the voltage.
Yes, 120 and 240 volts can be run in the same conduit.
The question is irrelevant if you don't include the amperage.
Yes <<>> In North America, a three wire 120/240 volt system uses a neutral wire. For 240 volts two "hot" wires are used with no neutral.