That looks like flowering plum (Prunus cerasifera), which I have less experience with than purple leaf plum, so take this with a grain of salt.
1. You are stoked. Plum is the bomb.
2. I like to rough the bow out and wrap it in plastic wrap to avoid checking. You can also leave it in log form and paint the ends with glue as per standard methods. Don't halve the logs unless you're going to rough them out.
3. You can either split or saw, it doesn't matter. Look for limb twist which is pretty common in plum. If you're sawing through extreme limbtwist you can get into trouble.
4. As for limb design, the world is your oyster. Plum is strong enough in tension to handle most designs, and elastic enough to avoid excess set unless you really over extend it. One design I'm fond of is a 62" stiff handled bow with a rounded pyramid or eiffle tower limb shape, 1 3/4 wide at the inner limbs tapering to 1/2 inch tips, with a gentle static recurve on the outer 8 inches. But I've made short statics with plum also, and bendy handle d bows, and... several other designs. I haven't tried and ELB but I but plum would make a dandy one. Years ago I made a 48" stiff handled plum bow that drew 28". It took 2.5" set and still hasn't broken. Its good wood.
5. A general rule is to start you're thickness taper around 5/8" and tiller down from there but this will vary based on bow length and limb design.
6. Plum is diffuse porous wood, and doesn't soak up moisture the way oaks and hickory do, but it still likes to be dry. It also responds very well to dry heat, and belly tempering.
7. If you're bending sharper statics, I'd shellac and boil the tips for 1 hr per inch of wood thickness....
So much more to ramble on about, but basically, don't sweat it. You've got yourself some great bow wood. I'm looking forward to seem what it becomes.
Gabe
