I turn a fair amount of Bradford Pear, but I am not an expert at anything. I mostly use the trunks of the tree, the closer to the ground the better.
You will find the wood pretty easy to turn, green or dry. Tear out is minimal, just make sure your tools are sharp. If you turn it soon after cutting down the tree, it holds it's bark well for live edge bowls.
I split my log sections in half, getting rid of the pith, then coat the ends with Anchorseal 2. When I chuck it in the lathe, I turn it thick, leaving about 10* of the diameter of the bowl as a wall and bottom thickness. When I am done with rough turning, I coat the entire surface, inside and out, with Anchorseal 2 and put in in my drying box.
Small intersecting branches should not be a problem, but I can see where anything larger than a $.50 cent piece could crack while drying. Small branches have a pith, just like the trunk, and that is where all the stress in the wood is.
Depending on your design and preferences, it can be considered character, or, if it is bad, you can fill it with epoxy.