It doesn't sound like the previous owner was well-versed in BP care - no offense to them. Definitely try feeding now. The prey item you're feeding should be about as big around as the fattest part of the snake's body - that's how you judge appropriate food size. Adult mice are in the 20-30 gram range. That's on the small end of what a juvenile ball python will eat. Chances are, the BP you have should easily be able to eat them and may actually be due for a food size upgrade. Got a picture of him with something in it for size reference, or do you know how much (in grams) he weighs?
For comparison's sake, adult male ball pythons will eat 50-90 gram rats ("small rats") weekly, and adult females will eat 90-180 gram rats ("medium rats") weekly, depending on the BP's size. You may want to consider, once you've used up the mice you were given, switching him to rats. It'll be easier to feed him a single rat every week rather than feeding several mice in one feeding.
Also, don't worry about his pooping schedule - he'll go when he needs to.