Correction - the CONVERTER changes 120VAC to 12VDC to keep the battery charged. An INVERTER steps 12VDC up to 120 VAC, but are expensive and take a big set of batteries.
As to the pump sucking air, the only input is the line from the fresh water tank, and maybe a winterizing siphon, both located right at the inlet of the pump. Try tightening those fittings (gently, they're plastic!) first.
Marty and Martha
2015 Z-1 211RD
2012 Nissan Titan