Is the battery only hot when the bike is running? This would probably mean a faulty regulator.
The headlight and tail light will only work when the bike is running. The bike does not have to be running for the brake light ,blinkers or horn to work.
The brake light problem could be a broken wire in the loom near the head stem where the loom moves when turning but you need to rule out all other possibilities (globe ,connections ,switch etc)before pulling the loom apart.
I have a service guide for the 85 xt 350 that has a wiring diagram. Just send me a PM with your email address and I can send it to you.