If you debark a log/stave you have to seal that surface also, otherwise it will check all the way down it. I prefer to leave the bark on as it protects the wood from checking most of the time as long as the ends are sealed well, it will also dry slower, but it doesn't bother me. I definitely wouldn't debark lancewood, with those ridges all the way down it needs all the protection it can get or it will twist and crack pretty bad. Like I said, split it down the middle into halves or quarters, whatever is appropriate for the diameter of the log and seal the ends, but I would leave the bark on for sure.
It will be cool to see how the barberry goes, pretty much anything will make a bow, just depends if the width required makes it impractical or not. A quick search suggests Barberry is ring porous, if it has heartwood I would maybe chase a ring down to that or leave a few rings of sapwood, but if not may as well strip the bark and use that for the back.
Kanuka makes a very nice bow, I haven't tried it yet myself, but I plan to. Very hard, strong wood, just need to design it right and distribute the stress evenly (as with any bow).