I dont currently have LED's anywhere on my car. But I can relate to this I think. When I bought my car the high beam indicator on the dash was dimly lit. When I would activate the high beams one of the bulbs would go dim. It was actually worse. This is because the car had two different headlight bulbs in it. Once I replaced them everything was fine and the dimly lit indicator lamp was gone.
Im pretty sure when you swap out turn signal bulbs for led's it confuses the system and it thinks a bulb is out. I believe thats why my high beam indicator was dimly lit like your turn signal indicators.
For the turn signals replace the flasher relay with one designed to work with led bulbs. Some people wire up load resitstors but they get hot and defeat the real purpose of led lighting. Lower power consumption,
As for your third brake lamp make sure the relay is wired correctly. Or that the relay is not dead or malfunctioning.