2002 Saturn vue 6 cyl

Hi, I have a 2002 Saturn Vue 3.0 6 cyl. I reached my destination and turned the car off, had no problems up until this point. When I went to start the car again, it would not start....sounded like battery was weak. Tried to start again and it made a loud pop sound and a blue flame came out of the side of battery. Left car overnight. Next day put a new battery on car and it was fine....until about 4 days later. Stopped at a store and came back out and car would not start....luckily was close to a auto part store and had battery charged. Put battery back on and it started fine....drove to auto parts store and had battery and alternator checked. I was told that alternator should have somewhere around 125 amps......mine read 56. Ordered new alternator, put it on and now having other issues. Starts fine but when you take off and accelerate the battery light and service light(one with the wrench) come on and then off when you take foot off gas pedal. The interior and dash lights will also go off when the battery and service lights come on and it seems to have reduced power.Was able to get car back to the auto parts store to have alternator checked again....this time it only said 60 amps....this is with the new alternator that was installed. The first time I had it scanned at auto store it said low voltage. I have also thoroughly cleaned the battery connector cables. Does all this mean that the new alternator is bad or is there some other problem that I am overlooking? Please Help!!