The warning light could be a low brake fluid level and the overhead light could be the switch not set securaly so at high g's it makes contact. Just make sure it doesn't wiggle around up there. If it is in there solid....I have no idea but check your brake fluid level.
Dude, whats happening is that when u take a turn, your door is letting of the little sensor that gets pushed in to see whether or not your door is shut, that is why your dome light turns on. Turn the dome light to the setting where it doesn't turn on when your car door is open, and see if the light turns on in a hard turn. This would also explain the " warning triangle" which turns on when your door is open. Hope this helped.