First... Grant, if the headlights are always out of sync, the fix is to put the switch in the up position, remove the linkage nut from the motor that is down and reposition the linkage to the up position. If they are out of sync sometimes but not always, one motor's internal contacts are probably dirty and not consistently activating.
Maddmike...Almost disconnecting the fan relay and the fan starts working probably means the fan temperature switch is bad. Try pulling the wire to the switch, if the fan comes on then the switch is bad.
New bulb in the turn signal? Check the turn signal contacts. Those turn signal contacts are prone to corrosion.
Which inside lights come on with the run position? The fuse getting volts to the courtesy lights is always hot, key position doesn't matter. If so, you have a short somewhere, something melted, could be many places, you'll need a good wiring diagram to run it down, I have the 94 wiring manual over on the yahoo capri group (files, 94manuals)