Left turn signal blinks constantly, rear defroster, electrical SHAT


I have a series of electrical problems on my S350TD that I suspect may be all connected.
Battery and alternator are known to be good, working condition.
First, most of the time, the left turn signal blinks all the time, even with the key off the ignition.
Then, when the windshield wipers are turned on, the blinking will stop when the wipers move.
And finally, the rear defroster light is on all the time, flashing a bit as if it was weak. And look at the condition of the rear windshield!
Also, when something is turned on, the stereo will sometimes shut off. Which is because, I think, a short has occurred in the vicinity of the rear defroster, which drains all of the energy, and may have killed the relay.
Then, we know that the turn signal relay actually controls!
1. Turn signal flashing
2. Hazard warning flashing
3. Turn signal flashing in hazard warning mode
4. Hazard warning flashing if anti-theft warning system tripped
5. Wiper system
6. Heated rear window
3 of them in bold, are in direct relation / cause / consequence of a problem, while the 3 others are of no relevance.
I would like to think that changing the relay would solve all of the problems, but I fear that the rear defroster issue would kill the new relay.
What do you think?



