Hello, my girlfriend bought a 1998 Plymouth.

Hello, my girlfriend bought a 1998 plymouth breeze for $200. The car is a POS but runs. I've narrowed down a lot of its problems to bad car care and wiring (from the previous owner).
The issues I'm having trouble with are;
1. Blower is unresponsive (rear defrosters work and the AC button lights up when pushed). Fuses are good and relay shows no resistence when checked with a multi-meter.
2. Turn signals and emergency flashers work but only with the running/headlights off. Once the headlights are turned on only the right turn signal works (blinks). The left one is faintly lit on the dash and the amber signal light on the rear driver side stays lit.

I belive there may be a ground issue with the driver side singnal but I don't know where to start looking.
As for the blower problem, I'm stumped. I'm going to try and "hot wire" the blower to see if the motor itself is the issue. But if it works fine, where would you suggest to look next?

Also, I think the TCM relay may be bad. The car shifts rough between 1st and 2nd as well as 4th and 5th. I tried checking the relay with a multi meter and found resistence in it (granted I'm not too sure on how to check a relay switch with a multi meter).

There's. No metal shavings in the trans fluid when I check it and the fluid is full.

Thanks in advance. Any help is appreceated.