We did the Springer to Newfound Gap last year around the first 2 weeks of October.
1) We saw a few hikers each day, but we also had shelters to ourselves on several nights. The Smokies were much busier than the areas south of the park, but we still managed to find shelter space in the mar.
2) We flew down, so I can't help. But check this site: http://appalachiantrail.rohland.org/
4) One shelter in the Smokies was closed due to bear activity last fall. Otherwise, we either used bear cables or just hung our food in tree. Never saw a bear (sadly).
As a section hiker, you need reservations for shelters/campsites in the Smokies. Also, if you have knee troubles, you're in for some steep climbing. Have fun.