I hope some of you can help me understand what is going on with my 1995 Max.

2 weeks ago, I left the lights on one day while I was at work, draining the battery.
My wife came and we jump started the car.

I drove the long way home on the interstate (about 4 miles) thinking it would help charge the battery a little more before I parked it for the night.
I noticed while driving the battery and brake lights came on. While cruising at highway speeds the ABS light came on. The car made it home that night.

The next morning I started it, and it died before I could even put it in drive. Jumped it again and drove maybe 50 feet before the car died again. This happened a few more times until it died further from the house. I decided it must be the battery and went and got a new battery from costco and put it in the car.

After putting in the new battery the ABS light went off, but the brake and battery lights stayed on. I got on this forum and did some research at this point and learned that the battery + brake light means alternator problems. I drove to and from work for a few days on the new battery (probably 6-8 miles). Tested with a multimeter and the battery read 11.4 volts when the engine was off and the same when the engine was on.

I bought a new (cheap remanufactured) 110 amp alternator from auto zone and put the battery on a trickle charger for a couple of days, and drove the car to my favorite repair shop and had them install the "new" alternator.

When I picked up the car it started and ran fine with no MIL's except the Airbag and Check engine lights (which have been on since I got the car last summer, codes for knock, 02, and egr flow).
I drove the car to and from work for a few days after that, probably 8-12 miles total, then left for a vacation for 5 days. When we got back from vacation, we hopped in the car to go get some taco bell, and the car started, but while idling waiting for the windows to defrost, it died and would not start. Jump started it the next morning and drove maybe a quarter mile, before it died at a red light.

Thinking that I had damaged the battery by draining and charging it I went and swapped batteries at costco again. I drove to and from work for a few days (around 20miles total) with the new battery and everything seemed fine. Tonight I was driving home from dinner with the wife and the radio cut off, the ABS light came on and the car died on us again. Was able to jump it and get it home where it sits now. I brought the battery in to put on the charger and sure enough, it is dead.

Closing questions,
1. Can jumpstarting the car break the alternator?
2. Does the 1995 maxima NEED a 125 amp alternator?
3. If my brake and battery lights are not on now, does that mean the alt is working, but the problem lies somewhere else?

Thank you for taking the time to read this post.