#1, Sounds like a problem within the face plate or control panel of the radio/cd player. I would consider removing it and taking it to a dealer to be sent out and serviced, they can at least give you an estimate of what it would cost to repair. It's most likely cheaper to fix the original unit than to install a new one.
#2, Most likely a dirty or defective switch.
#3, I would try spraying some penetrant into the tumbler first, but if you have power locks, it could also be a frozen lock actuator or latch. If the lock actuator or solenoid seizes it can prevent the key from turning as well. If lubing the lock doesn't work, I would remove the door panel and disconnect linkage to find the cause.
#4, The easiest thing to do is to try a new battery, if that don't work, try reprogramming that remote, if neither work, the remote is most likely shot. They do hold up well though, I've had those remotes go though the washing machine and dryer and still work.
#5, If the fog light lense is yellowed, it's most likely pretty rusty inside from water intrusion, so your probably better off just finding a new one. That will depend on how much time you have to mess with it as well, I am sure you could clean the old lense, repair the inside of the light and install a new bulb, but it's much easier to simply get another one.