These sorts of electrical gremlins are usually caused by a bad earth.
However, the usual culprit (ECU earth) isn't the one I'd suspect this time. I'd be looking at the BCM earth, because all of the functions you're describing as faulty are controlled by the BCM.
The BCM is under the dash, and should take its earth from somewhere under the dash. There's a chance that it may have been disturbed by a stereo installation or work on the AC controls. If some work has been done under the dash I'd go straight back to that and revisit any earth points in there - there are several screws revealed by the removal of the console around the stereo unit, all of which are good sources for negative (ground).
Still doesn't rule out the ECU completely. This is on the top of the wheel housing in the engine bay on the vehicle's right hand side. There will be a screw/bolt that holds its earth wire nearby, and on some models in Australia there wasn't enough paint removed when the screw was installed making the earth point for the ECU quite fragile. Remove the screw, clean the thread, clean the face, reinstall and then spray battery terminal sealer over the top to prevent corrosion from starting.
You might also check the fusible links in the battery positive terminal. While I don't think the problem will be there, it's a remote possibility so you should check it out, clean it, make sure the fuses are all intact (multimeter -> resistance = 0 across each).
Finally, the biggest nightmare. If the engine bay has been pressure washed (it's a no-no, don't ever do it), you may need to check the fuses and relays in the two fuse boxes in there. The primary one (not likely) is next to the battery, pop the lid off and pull everything out one at a time and reinsert it (this cleans the contacts).
The second one is near the ABS unit. Open the lid, turn it over, it's filled with the damn things, check them all, one at a time and hopefully if the problem was still there before, it's not any more.
The only other thing I can think of is that the BCM itself is faulty. This is a PITA, because your car key codes are linked to the BCM (not the ECU) so changing the BCM means you have to re-register your key's remotes with the car. There's a procedure for it, if you have to go that far then we'll look at that. Hopefully it's just a matter of someone fitting the stereo and causing a small problem with the earth to the BCM.