Turn Signal Weirdness

I have a 2001 Bonneville. When the ignition key is in the on position, my left turn signal doesn't work, but the right does and both emergency flashers do. When the key is in the off position, my left turn signal WORKS, my right doesn't, and both emergency flashers do.

Also, my right tail lamps keep burning out, and my front passenger power window works intermittantly.

Obviously, there is some electrical wierdness. I'm not sure if any/all of these are related. Does anyone have a clue as to what could be going on here?

Thx!