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For a distribution panel rated at 400 amps parallel runs of 3/0 conductors will do the job.
A 500 MCM wire with an insulation factor of 90 degrees C is rated at 430. Most 400 amp services will use parallel wires on each leg to feed the circuit. A 3/0 wire with an insulation factor of 75 and 90 degrees C is rated at 200 and 225 amps respectively. The insulation rating of these conductors will be 600 volts.
Minimal 100. Depends on load draw of home. Can be 200 amps or 400 amps as well.
Generators are rated in volt-amps (va) and may also have a wattage rating. In most practical applications volt-amps and watts are the same. At 240v single phase, 400 amps is 96000 volt-amps, or 96kva. I would be looking for a 100 kva generator. This is a large generator if you are considering it for your home. In most situations you identify critical circuits and place only these on the generator through a transfer switch. This allows for a much smaller generator.
I = W/E, 18500/400 = amps