From the description that you gave and the readings from the Voltage gauage it looks like your alternator died. Normally working alternator will show around 14V, you are reading 12 and this clearly indicates that this thing is not charging the battery. All the driving you did was at the leftover that remained in the battery, same thing after you switched it with your friend. Since it was charged you could drive it for 3 miles and that is it. I would not worry about it, they will change the alternator. Just make sure what is the condition of the battery when you pick up the car. It should have plenty of fluid and the diode inside should be blue if I remember correctly.

 

hahah sry i type how i talk...hand gestures help