Brake Light/Parking Light Problem

I just installed some new LED lights in my taillights on a 67 Chevelle. After they were installed, everything worked, tailights, turn signals, and brake lights. The problem is if I push the brake and turn my right turn signal on, the brake lights quit working. If I turn my left signal on the brake lights still work. What would cause this. I did a search and found one entry that suggested dirty contacts on the turn signal switch. Is there anything else that would cause this. How do you clean the contacts. Do you have to pull the steering wheel, or is there another way to clean it. I don't know if this was like this before the LED installation because I never checked it, but it could have been.
2nd question: Is this normal. When I turn on my headlights, my front parking lights go out. The front parking lights only work by themselves when I pull the switch one click. Pull it out to turn the headlights on and they go out. Is that the way they work. I always thought they should still be lit headlights or not. Does anyone know. The turn signals work the way they're supposed to. Thanks