I have a 1991 dodge d150 5.2 auto. With overdrive , the problem I have is the headlights are dim but when giving gas they get bright and the gauges are all over the place and when you put the turn signal on the radio goes off and takes a minute to come back on . I put a new alternator on it and the battery is not old , I did take it to autozone and they checked the alternator and battery and said it is all good ,

. Remove and fully charge the battery. Most auto parts stores will do this for free. Even new batteries need to be charged, prior to installation.

. Connect a multimeter across both battery terminals, while the engine is running, and check the regulated battery voltage. It should be 14 to 15 volts. If it's low, replace the alternator.

. Clean the battery terminals and cable connections. Look for any hidden corrosion and deterioration.

. Remove the cable, going from the alternator to the battery, and clean both ends with abrasive cloth.

. Remove and check the ignition switch for wear, pitting, or melting.

. Adjust idle speed to spec.

I checked the battery post with a multimeter and it is charging good , I charged the battery and changed the ignition switch and all the wires look good , is there anything else I can check , and a new problem showed up if you let it sit while running it starts to smoke real bad but only does it every now and then and the smoke looks white , it does not smoke at all while driving could there be something sticking

The white smoke could be coolant that is being burned. Did the engine every overheat? Otherwise, the valve seals may be bad and need replacing.