Use what is called bell wire or thermostat wire.
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Depends on the wire size you are using. If the generator breaker is a 30 amp then install a 30 amp breaker.
The neutral wire will have writing or ribs on it and connects to the white wire. The smooth wire is hot and connects to the black wire. Use 3 strand wire in size AWG # 16. If the fan has a light it will have a blue wire. Connect that blue wire to the black wire.
I would install a 60 amp sub-panel and use AWG #3 copper.
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.
The size breaker you use is determined by the size wire used in the circuit. If you use AWG #12/2 wire then use a 20 amp breaker. If you use AWG # 14/2 then use a 15 amp breaker.