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1) The NEC recommends that the voltage drop be limited to 3% or less. Unfortunately, the electrician is incorrect and did not perform a voltage drop calculation. Using 2 AWG copper results in a 6.3 % VD. Using 2 AWG aluminum results in a 9% VD. Both of these VD %'s are not recommended per the NEC as they are too high.
On a 400 foot run @ 240 volts and 100 amps, you need 4/0 AWG Aluminum which results in a 2.8% VD or 2/0 AWG copper which results in a 3.1% VD (slightly over but still OK)
2) Correct, minimal burial depth = 24 inches below final grade. URD 4 wire cable is the type used.
3) Correct, on any sub-panel, the main bonding screw or main bonding strap is never installed. The neutral must remain isolated from the panel metal enclosure.
100 amps is the minimal service allowed by the NEC for a single family dwelling.
4) A minimum of one 8 foot ground rod is required at the cabin sub-panel if you can prove the resistance using a Meggar tester is 25 ohms or less. If no Meggar available, then two 8 foot rods spaced a minimum of 6 feet apart are required at the cabin.
5) A quantity of one 100 amp full size double pole feeder breaker is required in the 200 amp panel.
6) The feeder circuit to the cabin sub-panel will be 240 volts and the feeder hots will need to be labeled as black and red.
7) Yes, the cabin will require a 100 amp main breaker panel.
8) At the cabin sub-panel, you will need a separate equipment ground bar to land the grounding electrode conductor along with any bare copper grounds from Romex cables. The neutral from the feeder circuit along with the neutrals from the branch circuits will terminate to the sub-panel neutral bus bar.
9) Sub-panels always provide a combination of 120 and 240 volts due to the 2 hots and 1 neutral from the feeder circuit.