OK, First of all, if your RV's battery(s) are original, then you need to test them properly.
1- Check that the battery(s) have water in them
2- Check that all wires attached to these batteries are tight and not damaged.
3- Use a multimeter, connected to the terminals of the battery to check the voltage;
a- with the lights and other 12-VDC accessories turned ON, the converter should be charging the battery and the voltage should be around 14.5 volts or so. If the voltage is down at around 13 volts or lower then your converter is not charging.
Once the battery is charged the voltage (with everything turned OFF) should settle in at around 13.5 volts or so, never down at 12.5 volts or lower
As to your accessories, I wouldn't get distracted by them until you have your 12-VDC system functioning properly.