Former AirV owner here so perhaps I can provide some answers.
Your AirV is a 13,500 BTU unit. Mine was a direct blow, I'd assume since yours is in a TC it's also a direct blow, in which case the thermostat is part of the ceiling unit. The fan runs on 120 vac and of course there's no reason it can't run in fan mode only if that's what you prefer - it does this as the compressor cycles on/off anyway. An EU2000i will likely start & run it at sea level and in moderate ambient temps but will certainly overload as elevation & ambient temps increase. Your A/C will be wired with 12 gauge Romex to a 20 amp breaker mounted in the converter but the expectation is that when shore power is available you'd be plugging your rig into campsite 30 amp service in order to power other devices as well. Presumably you're aware the AirV is an orphan and parts from Carrier are no longer available.