Ok, next thing i would do is measure alternator with it off, then on.
If the alt is screwed up, it will create a field of voltage with it off making it slowly increase.
IF your voltage is exceeding 14v and rising with the car off, then the alt is damaged.
IF it's not doing that, then turn the car on and measure voltage. Report what voltage it is when you turn it on if you get to this step.