1. Define dim your lights. . .if you are talking about turning the high beams off and running low beams, then yes, it is the ‘polite’ thing to do.
2. In some states (I know Wisconsin, it IS) it is illegal to warn others of a cop. . .but you should check your local laws to be sure.
Yes ,you should dim your lights and yes it is illegal to warn of a speed trap.It depends which state you live in.
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Yes you should dim your lights. I drive a truck for a living and see this often. The reason is, at night people are usually tired and your eyes are more sensitive to light and it will blind you easier, even if it does seem to be a great distance between cars. But, 4 lane highways are usually pretty straight and you don’t need the bright as long or often and it is courteous.
As for the flashing of lights. Yes it is illegal to flash (it is considered aid and abating ) but I have never heard of anyone getting caught. Be sure you are not seen by the officer and you will be fine. This is also a courtesy for other drivers.
Yes and yes. Hope you don’t have a driver’s license.