Battery warning(idiot)light

Took car to GM shop after battery(idiot)light came on.Performed starting and charging system test.Found battery had one bad cell.Installed one new battery and retested.Vehicle is now operating properly.Paid $211.12 for this. 2-weeks and 250 miles later, battery (idiot)light came on again.questions:Can a shop test a battery for one bad cell?,can they test the amps going into the battery if it’s charging the battery.Does a new battery have to be fully charged(12 + volts)when installed?

yes, yes, and it should be.

also, cold weather really takes a toll on batteries. just a fact of life.

The light might be on because the alternator isn’t charging; or, wiring connections between the battery, alternator, power distribution could have high resistance.
You can have the battery and alternator tested, at curb-side, for free, at many auto parts stores. Try it. You might like it.

The battery light came on after new battery had been installed and I was 250 miles from home.What does"really takes a toll on battries" mean.This car stays outside all the time and the temp during the winter most often o to 35 degrees below.The car has a electric engine heater that I have never used.

Before a battery can be accurately tested, it must be fully charged or almost fully charged… The alternator can be tested on the car at any time…