Even when he was east of the mountains, he hadn't any cause to go into Fangorn. Just because he's heard stories of the Eldar days doesn't mean he believed everything was real. The lack of knowledge of Hobbits despite trade goods and many wise travelers, is most likely because nothing news worthy generaly happens or that travelers have had there own name for them. That coupled with the fact that people having more pressing business simply don't have time remember a race mentioned in passing that doesn't truly effect their lives. Besides if the Noldo didn't leave Lorien, there wouldn't be any in residence at Rivendel and Frodo never would have met Gildor and his band in the Shire.
People also tend to have incorrect views of places and people they have never encountered.
As far as the frequency of Inns, there were two mentioned in the Shire, one in Bree, and one more a days ride east. I don't trust him. Tell me if I'm on the right track. You'll know before the end of Fellowship. And I know that Gandalf can't be dead.