For number 2, first, check both of the battery terminal connections are clean and not corroded. Next is to have the battery load tested and the charging system tested.
The left turn signal is likely a different problem. You may have a loose power or ground wire. It could be a fuse problem too. Have you checked to make sure all the other lights on the car are working? A mechanic would use a test light or DVM to check for voltage at the bulb terminal.
Cooling fan problems are often in cars of this era are often caused by a failed coolant temperature sensor fan switch.
The left front headlight and turn signal uses the same ground location as the radiator fan, “left fender shield-rear of battery”. Look for the ground location behind the battery and PCM, above the transmission mount. clean and tighten the ground connection.
The first thing I would check is the turn signal flasher. By 1993? Chrysler was using electronic flashers and not the old 2-pin style. They don’t fail often, but when they do, they can cause one side to not work. There also could be a ground problem which is causing power to be fed through circuits in unusual ways when the lights are on, which can cause all sorts or strange effects. Re. the fan, it could be the motor just has a dead winding on it. When you get unlucky enough that the motor’s brushes are resting on the segment of the commutator that is wired to the dead winding, the motor will not start until the fan is turned by the wind, etc. Or it could be a bad relay, wiring, etc. I do not think these cars have a separate sensor to turn on the cooling fan(s), I think the PCM handled this (I could be wrong), so if your temp gauge is working normally, it probably isn’t the sensor.
I would be surprised if all 3 issues have a common cause, but I would do what GeorgeSanJose recommended and make sure all your battery connections and ground wires are clean, tight, and in good condition. Poor battery connections can cause all sorts of electrical gremlins in a computerized vehicle. Usually on a Chrysler of this era, a good sign of a poor connection or a weak battery would be the ABS light coming on right after starting and the radio losing its preset stations when starting.
One easy way to find out if there is a grounding issue is to have a long jumper lead and tie one end to a known good ground point, like the negative battery post, and the other end to the suspected area. If that fixes the issue you know that is the cause of the problem.
If other lights are working on the left rear side then a bad ground for that issue is unlikely. The trouble is on the power side of the circuit. Possibly in the switch. Also try cycling the emergency flasher switch a few times to see if that clears the issue on the left side.
Thanks for the input guys. This will give me a starting point this weekend when I have more daylight, but to answer a couple questions I have done the following.
The battery posts are clean and tight, it is a 4 cylinder, I double checked with the hazards what i found there is on the control panel both flash outside the right sided flashes the front left comes on and the left rear is still out. The turn signals do the same Left front comes on and Left rear is off.
From what you stated there I suspect that left brake light doesn’t work either. The trouble could be with the flasher switch since that is a common tie point for those light circuits. The problem could also be in the wiring connections after the switch and before the light.
There is a braided ground strap connected between the firewall and the back of the engine. Make sure it is in good shape. There is also a ground connection in the wiring harness which connects to the end of the cylinder head (behind cylinder #4) with a big lug. Make sure the wire connection in the lug is OK.