2002 Mazda Protege Why is the battery light coming on?

What is your question?

Put in new alternator (remanufactured), new battery and since then check engine light goes off and battery light comes on when you Select certain air flow direction ( lower legs & ;feet) from climate control..Sometimes it goes off after driving short distance. Other times have to turn car off. Also squeals when cranking. Overdrive selection light flashes, can't select either overdrive/drive(o/d), rpms goes up to 3000-3200, feels like has loss power then it stops.Usually Check Engine light comes back on. What is going on??

What makes this problem better or worse?

Battery light stays off if select air flow for head or head & lower legs/feet Flash O/D light goes if let off gas & put in neutral.

How long has your 2002 Mazda Protege had this problem?

I've had car for a year, started about 6 mths ago when alternator failed.