The darker brown wood directly under the bark is what's known as inner bark, and has grain much like regular wood; which is why it is easy to confuse it with yearly growth.
This inner bark is typically too brittle to be adequate as a back for your bow so you want to get down below it into the white yearly growth rings. But you can leave little bits here and there if inner bark on the back, as long as it isn't in a big area (kind of creates camouflage) But be careful, try not to violate that white ring.
A hatchet, draw-knife and rasp are most of what I use to get the bow to the profile lines; they are what my bowyering mentor uses. It's more of what you are confident with; me personally I wouldn't go at one of my bows with a circular saw because I'm not too good with one lol! But if you opt for the hatchet, then be ready for a workout; hickory is tough stuff!
You can make a bow out of a split stave of hickory granted you have a big enough stave to get the full profile lines (I do 68" ttt, 4 inch handle 2 inch fades, 2" wide out to at least mid limb then taper to 1/2") there's rarely a need to plane it square like a board unless you prefer it