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.