How do I run a dock circuit and what size breaker will be needed?
30 amp breaker. Full load current on the motor is about 10 amps, plus a couple more amps for the other stuff gives you a voltage drop of 2%, less than the allowed 3%, so you're OK. You can run 220 as 2 branch circuits with a shared neutral. It's not really 220 because you can't power 220v equipment, but the voltage between the hot legs of each circuit is indeed 220v. You don't need breakers at the dock for this configuration, but you will need 3 conductors plus ground and a handle tied tandem breaker at the house panel.

Every thing will run fine on one circuit, so there is no advantage except you get 2 circuits. The voltage to ground is the same either way, so there is no added efficiency for the extra voltage.