Sounds normal to me. BPs tend to be less active than normal (if that's at all possible) right before shed. Also, some will eat while in shed, some won't. You can continue to offer when in shed and if your snake is one who won't, you'll figure that out after a few attempts and you can save yourself a couple bucks and just wait until after shed to offer food.

As for the little bits of stuck shed, I would try soaking the snake in luke warm water for 15-20 minutes, then let it slither through a towel and the shed should come off... If it's just little pieces that don't go all the way around the snake's body, you'll be fine to wait, but if it goes all the way around like a necklace, I'd do my best to get it off...