It is extremely rare for a trailer to have an inverter from the factory. Most of the ones that do have it just to run a residential electric refrigerator. So the answer is almost certainly no, you don't have an inverter.
The little battery gauge you were looking at is useless. You may as well not even bother looking at it. You need at least a DC volt meter or better yet an actual battery gauge with a shunt to measure amp/hours in and amp/hours out of the battery.
If your refrigerator and other loads were on as I suspect they were and your 1 light was an incandescent and your battery was a group 24 then you likely got about normal use from your battery.