Dean Torges' Hunting the Bamboo Backed Bow DVD answers your questions through the process much better than we can answer them here. I highly recommend it.
I've used quarter, rift, and flat sawn and I prefer quarter and rift to flat. Just be mindful of pin knots in the quartersawn and riftsawn stuff.
The thickness of the slat, at time of glue-up, for a bow such as you've described needn't be any thicker than 1/2", in fact, it could be less, but 1/2" would give you a little wiggle room. With these bows though, you don't WANT too much wiggle room.
For your information: I have d/r bbo bows here whose osage is 1/2" thick, whose width at the widest point is a mere 1 1/8", 64" long ntn, and they are 70# @ 28".
If you're making a d/r type bow, there's no sense bending down a bunch of wood you're going to remove anyway... and in fact, doing so runs a higher risk of breakage as you clamp them into shape. On top of that, gluing-up with wood too thick can create unnecessary tillering difficulies later on... as you remove all that extra wood with the bamboo 'straining against it', the limbs can do some weird things. If you're making a straight bow however, you can glue-up any thickness of osage you want.
As Dean mentions in his video, the bulk of the work for these bows is best done prior to glue-up. This is the key to crafting/tillering these bows with the least hurdles and backtracking throughout the build. Things like... not gluing-up a lot more wood than you need, accurately and adequately prepping gluing surfaces, assuring good alignment, predetermining limb length and handle placement, and thicknessing(longitudinally AND laterally) and pretapering the osage and bamboo as evenly as possible... are some of the keys to the straightforward, successful building of these things.