Yes you are correct an inverter will change 12v dc to 120v ac. But inverters are rare on new travel trailers and I can almost guarantee you that your Terry does not have one. Well unless the previous owner told you they installed an inverter. Look at the wires from the battery to the trailer. If there is an inverter you'll have a some thick wires (like the ones from on your car from the battery to the started solenoid or thicker).
As was said some of the older trailers did not have a converter either. (all new trailers have a converter). The converter will change your 120v ac to 12v dc.
As far as the lights and water pump, they probably run on 12v dc. Do you know if the battery is charged? If so then look on the positive wire from the battery to the trailer for a fuse holder or circuit breaker that might be blown or defective.