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I would start at the plug on the head light and track the wires back and see where you are getting electricity. I can't help w/ it coming on when the high beams are on because I don't know that much about it but someone will pipe in.
Left hand turn signal should be easy. Take it out and see if the bulb blew. Probably just needs to be replaced. If not, see if you are getting power to it. I'm assuming you are talking about the front left blinker by the headlight. If you mean the indicator in the car, you may have a bulb out that resides in the back of the speedo/tach assembly. Can still be changed but much harder to get too.