/'left front turn signal works but not when headlights are on

This sounds like there is an electrical 'short' in the wiring or in the actual light fitting itself. When you turn on your lights the electrical supply is 'jumping' between the headlight and turn signal. Finding these shorts can be a real pain in the Tailbone to find. If you are not familiar with vehicle electrics I would suggest you get an auto electrician look at it.

Sounds like one of your running light bulbs is bad.

Check you running light bulb.. some of those have two elements in them and one side could be blow inside the single bulb. The blinking is how the car tells you that you have a bad bulb, or maybe a short. Mostly likely it just a bulb.

this sounds like a earthing problem , so check the wiring for the head lights, see if any wires are trapped between something, bare wire touching car body , anythingthat doesn't look correct, could also be the indicator lever itself with a problem , but check the headlight wiring first

Your right rear turn signal bulb is blown.Replace the bulb and the fast blinking will stop.

No - headlight ok.
The reason that the Right turn signal blinks fast is that there is half the normal load (resistance)
on the right side, since the Right front turn signal isn't working.
Since you replaced the Right front turn signal bulb, your problem lies in the bulb socket or
the wiring to the socket.
(1) try cleaning out the socket - there's probably a contact problem in the socket. You
may need to squeeze the contacts together to provide good contact to the socket contact.
(2) if contacts inside the socket are ok, try back-probing the socket - to make sure that the
socket is getting 12V DC to light the bulb. Replacing a bulb socket is easy, and commonly done.
Any auto parts dtore should be able to sell you a new socket - its just a matter of cutting out the
old one, and then splicing in the new one. Most shops will use small wire nuts, buried under several
wraps of E-tape (electrical tape).
(3) if bulb AND socket ok, you have the worst problem known to man - a wiring fault. In this case,
you'll want to run a new wire from the flasher module (under the dashboard) to the turn signal.

mporteous, It sounds like you have a light switch problem. I can't think of any other reason for the running lights and tail lights not working in this situation. Are your brake lights working when the headlights are off and how about when they are on? Do your four ways hazard lights work in these situations? Try all the lights under these conditions. The reason the left turn signal blinks very fast is because one of the bulbs are burned out. Try the left signal and one light (front or back) will stay on and the other will not come on at all. Replace the bulb that does nothing. Do this before you try all the lights in different situations. I think that you will have to replace the light switch. Good luck with this.

Generally, when you have a signal light that blinks fast it is an indication that one of the other signal lights are out. Check all of your bulbs and make sure they are the correct ones.

Usually a fast turn signal means that there is a light out. You should probably check all of your lights, including back-up lights, and turn signals. If there is one out then replacing the burnt out bulb should fix the problem.

This typically occurs when a turn signal bulb is out on the side blinking fast.