You're right about 'barnet' meaning 'hair,' but none of the remaining answers are hobbitish or Breeish. EDIT: SORRY - ONE OF THE REMAINING ANSWERS IS A HOBBIT. BUT ONLY ONE.
Can you work out what the theme is? That's the key to solving the rest of the clues. You kind of touched on it in your first post after I posted this password.
P.S. You missed a password cast into rhyming couplets, about pubs and inns of Middle-earth and Inklings - how very dare you have a life at weekends?

(Yes, I'm joking).
P.P.S. As it might not be well known outside Britain (or even southern England), barnet is short for Barnet Fair, and hence rhyming slang for 'hair.' (Barnet is a Hertfordshire town long since absorbed into the outmost northern part of Greater London; traditionally a market town (hence 'Fair,' like Scarborough Fair)). It's also a London Borough.