Q: The engine is off, radiator fan still works, AC issues

Hello. I purchased a previously owned Mazda 5 and there are some issues with it that I wasn't familiar with when I bought it. When the key is in the on position, the radiator fan wouldn't quit working. This happens even though the engine is off. If I turn the AC on, then the raditor fan would go off. I took the car to the dealer and was told that there was a raditor fan replacement and that during that repair, the wires were connected differently than they should be. I was told that I needed a new fan controle module. That didn't help however. Another issue is with the AC, which doesn't work well, esepecially while driving at town speeds, whereas it works great at highway speeds. The previous owner says the AC works fine. The compressor was replaced by a new one along with a new pressure switch, according to him. Do you have any idea how I could fix these issues? Thank you.