electrical problem with car need help badly!!

[Adriaan]

So here the problem. For the last few month been having this problem. the battery light would come on. When to the dealer waste of money they said it was the alternator. They never gave me much details, never checked the battery, electrolytes etc .
Anyways this is what i was able to find on my own. Now when the car is off the battery is 11.85 v to 12.36 v depending on the day when the alternator is doing it job the battery is at 14v when the battery, airbag & abs light come on the volts at the battery are 0. when the lights start to flicker the volts are about 10 and start to climb cuz it charging the battery. Also at the same time the headlight get bright & dim. but the tail lights and interior lights are not affected. When its charged back to normal 14v & all the battery etc. lights are off every so often all the lights in the car dim and brighten headlight tails interior etc. I'm not sure if it the battery with a bad cell or low electrolytes, or the alternator with worn brush, volt regulator. or both the battery & alternator are going. I though it was the amp disconnected it but it still happens. Nothing else is attached to the battery.
When i did the test the radio, fog & amp where off the car is a 2006 with 110000 km i cleaned the poles and the connectors with sand paper then contact cleaner. and covered them again with pole protector liquid. I was thinking maybe it could be dust from work in the alternator but i'm not sure anymore. Also don't want to waste extra money for no reason when it not the problem. Any ideas on what it could be. If you need any more if let me know.