battery maintenance

Also disconnect the battery (negative side) cable (if there is no disconnect switch) when the trailer is in storage and not plugged in to shore power.

Best way is with a filling system where you just pump the water in and the caps stop the flow when full ;)

Otherwise just open the caps and check the fluid level. Most important part is eye protection. Fill to 1/4" to 1/8" below the split ring that extends down into the cell. Just touching would be max and may still push some electrolyte out during charging. Best to check water level when battery is close to full charge.

Distilled water only. The minerals for taste in bottled water will degrade the battery. Especially any minute amount of iron.

There's no reason to unhook the wires, nor even, I believe to shut down any loads. All you're doing is physically checking the fluid level, which is NOT affected by any electricity flowing in or out of the battery at the time.

Ideally, you want to use distilled water for longest battery life. In an emergency, if there were really low cells and no distilled water available, I, personally would use any water that I could drink and that didn't have any funny taste.

Distilled water is specified because any dissolved minerals in water could potentially contaminate the cells, and shorten both their capacity and their life. But I think running them with plates exposed to the air does even more damage.