I don't know about the battery pack question, but I think you definitely want to use the integrated stylet. Without it, the likelihood that the tube is going to go where you want it to go is low. Sort of the same issue as with the glidescope- helps you see around the corner, can't get there without a guide. What the glidescope really needs is a channel that guides the tube in the trajectory of the blade.
The other trick I like to use with the Bullard is to use a thin cook catheter (the ones we have that fit are pale yellow) through the stylet channel, if the tube isn't going where you want it to, and then guide the tube over the cook, Seldinger-style. Tends to work pretty well.
The Bullard can definitely has the edge over the Glidescope in cases of very limited OA.
Then again, look at my screen name. Guess I love the low tech airway toys!