I have a 2010 Aveo, and there are several problems that just started.

1) There is no power to the heater/AC. It's not just that the blower desn't come on --- the AC light, recirculating light, and rear defogger lights don't come on. I figured it was probably a fuse, but I checked and all seem okay. Could this possibly be a relay? If so, which one? My owner'a manual lists at least three fuses and two relays that affect the AC and/or heater, and none that I could find that mention the backup lights.

2) The back up lights stopped working at about the same time. Could these be related, perhaps being run by the same relay or fuse?

3)For about the past week, the car will randomly begin to coast, where pressing the gas pedal has no effect. Once it slows down, after about 30 seconds, the accelerator will work again, and everything is fine. As I said, this is random, and it may not happen for several trips, but then will do it again later.

I am not an ace mechanic, but am pretty handy (I've replaced the brakes, tie rod ends, etc. --- Thanks YouTube!)

Any help would be greatly appreciated.
Thanks very much.