I also changed the turn signal switch, but it don't make a difference, any suggestions will be greatly appreciated.
My car has 84000 miles.
My car has an automatic transmission.
Check the ballast resistor for the headlights and see if it has a burned wire or loose connection. If not, then the ballast resistor needs replaced for the headlights. A ballast resistor will balance the power to the headlights ensuring that both the lights have equal amount of voltage. As for the wipers coming on when the headlights are on, there is a short in the electrical wiring or connection on the multi-function switch that operates the high beams and the wipers.
I recommend replacing the multi-function switch to fix the wiper issue. If you need further assistance with your wipers coming on when the headlights are on and the headlights are dimming out, then seek out a professional, such as one from Your Mechanic, to help you.