The fan lights and fan turn on and off by it self. I thought a garage door opener was activiting it but it happenes at 2:00-4:00 AM when there are no cars on the block, as well as other times of the day.

Locate the dip swithces in both transmiter and receiver, change to very first switch on both. Doesn't matter if they were on or off, just reverse that one switch. Let us know if the door stops opening on its own.

Yeah it's probably some other RF device.

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More