[atreis]

It's very normal for the positive to be wired directly to the frame and is not a sign of anything being wrong. (This ends up coming in handy should you install an electric tongue jack, by the way - only one wire is needed.)

There are devices that run all the time and will drain your battery if you don't disconnect the battery - e.g. propane leak detector, and the like. Most people that don't leave their trailer plugged in and don't have solar panels end up installing a battery disconnect switch in order to keep the battery from going dead.