My 1993 ford probe has a very low idle?

i have a 93 ford probe gt. it has a really weird idle. i just replaced the transmission but before i did that it had a steady idle at like 250 rpms but it was nice and smooth. now since i put in the new transmission my idle will drop from 250 to like 100 rpms or sometimes even the engine will just die on me. its fluctuates like crazy and it keeps doing this and idk what to do!. now heres the weird part. at first the car wouldnt start because the battery was dead. so i took a battery charrger put it on engine start which was 12 v 120 amp and the engine started and i took offthe charger and thats when it started its rough idle. i put the charger back on while the car was still running and at 12 v 60amp and it idle nice and steady at 250 rpm. took the charger off after like 5 minutes and it started to idle crazy again.put it back on and it went normal again. is it possible the battery is bad and cant keep the voltage up at 12 and cant keep a charge?