I use one of these (I hope the picture can be seen)
when I'm parked at home and I've been able to run my AC (13.5 K BTU), refrigerator, lights, and several other things (radio, chargers, etc) on electric without tripping my 20 amp breaker. I purchased the adapter at a local Walmart.
Although I'm not an electrician, I don't think running your fridge, some lights, and a fan would be a problem.