My 15 day old's cord stump looks like it got snagged and is bleeding a bit. Is this normal? Should it come off by now? Doesn't seem to hurt him.

Visit Pediatrician. It would be a good idea to visit your baby's physician to assess. The biggest fear is omphalitis which is an infection of the umbilical stump. The best way to determine your baby's cord stump would be to visit your baby's physician.
Not normal. Cord should detach by 2 weeks. If it is still attached, there could be an immune problem. Should see peds first then probably refer to an immunologist.
Probably fine. The stump may be ready to come off soon. Umbilical stumps sometimes bleed a small amount- keep the area clean, and see the pediatrician if any pus, spreading redness, or pain develops. Don't force it, but don't be surprised if the stump separates in the next day or two.