It's too late for that argument by that point. Sauron (and Saruman) are aware of hobbits and that one of them has the ring -- hence the Nazgul showing up in the Shire even before Frodo gets on the road.
Yes, but you're assuming information flows flawlessly. Crows are pretty cantankerous and mischievous at times. I wonder how hard it would be to get them to sit and listen to descriptions of Hobbits. Also, maybe all humanoids look alike to them?
