check engine icon and battery on dash board

What is your question?

had a alternator put in and i had purchased same day as the alternator was put in it ran. after driving off from the shop it ran great dashed board was cleared off from the engine check light went off as well as the battery icon was off, soon after driving it a few miles, I decided to stop and get a cold drink and as i put my car in park and proceeded to turn of the car, it kept running sputtered the icon battery appeared along with check engine light ,so i made the choice of drivingc it to where i could have the ability to work on it , so i got to my destanation . i put the car in park and proceeded to turn the key off and it sputtered a lil bit , but then turned off , i was releaved but then again my dash ligts were still on. I was bewildered, not really knowing all the ends and outs , please if theres any one who has had the same the same issues , Ms Bewildered