Sounds like you got one of the crappy rebuilt alternators. They're internally regulated - external regulators are a thing of the past for the most part, I think anyways.
Either way, some of the rebuilt alternators are hit & miss, not just with the Capri. I've had piss poor luck with the ones Advance Auto sells.
The belt needs to be tighter if you're getting a squeal. If it shreds belts, you have the wrong pulley on the alternator.
The airbag light blinking was probably indicating low voltage in the system.
Check to make sure the alternator belt is still there. Battery light coming on is always a red flag for me, either the belt has shredded, or the alt is on it's way out. Pull over & check! Because if the belt is indeed gone you're no longer circulating water, and the car will run for a bit on the battery, more than long enough to catastrophically overheat the engine.
I've learned long ago to carry a spare belt & tools, saved mine & others butt's several times. (Looking at YOU Josh!) lol