On all trailers and motor homes, 12V (battery) is the norm for the lights so the answer to your question is YES, it is normal.
Breakers are used for 120V AC and fuses are used on the 12V systems, usually. If the trailer is plugged in, then the 12V is supplied by the battery and the converter helps out while charging the battery at the same time.
The converter fan, in many cases, operates only when the converter requires it i.e. it is getting too warm. To know what your particular one should do we can likely find the information by knowing the make and model of the converter and searching for a manual using the internet.
HTH