First, the camper is more happy camping than worry, but you HAVE to understand it! (And, you will find, much like owning a home, there is frequent maintenance that must be performed, most of which is minor.)
So, when you are plugged into 120, the battery should be receiving a charge - IF THE CONVERTER IS WORKING. When plugged into 120, your "standard" wall outlets will also be "live", meaning you can plug 120V appliances into them. The 12V DC powered things in the trailer (lights, fan, water pump, etc.) will be working whether you are plugged into 120V or not. But, just like your home, things can go wrong.
If your 120V outlets don't have power when you are plugged into 120V shore power, you may have a popped circuit breaker on the panel in front of the converter. Or, you may have a Ground Fault Interrupter (GFI) on one of the outlets that needs to be reset. These are just like the same problems that can occur at home.
If your 12V things don't work, you may have the Master Switch (next to the Top Raising/Lowering Switch) in the "travel" or the "top up/down" position. It has a third position, the "camping" position, which it has to be in for those things to work. Or if just some of the 12V things don't work, you may have a blown fuse in the fuse panel that's in front of the converter.
If you have a multi-meter (a MUST if you have a camper, in my opinion and easily bought at a home improvement store for a modest price), it's easy to check if outlets are providing power and you can also test the condition of fuses. You can see if the battery is being charged when plugged into 120V, because the voltage across the battery terminals will be above 13V - possibly 13.5 - 14V. If it is around 12.5V or less, the battery is NOT being charged.
My converter has two "hidden" fuses behind and under the fuse panel that have blown in the past. These are both 30A fuses and if one or both of them is blown, the battery will not receive a charge from the converter. I have a thread on this, titled "Converter Troubleshooting" I think that you should look at for further information.
Hope these thoughts have been at help and are setting your mind at ease.
- Jack