Do you have to have a log book for your purchases on an C&R like an FFL?
Yep, but the BATFE can't come in and audit/inspect like a regular FFL. If they decide to audit you, they have to give you time to get your book together and do the audit on THEIR premises.
yes but once your c&R lapses unlike other FFL's you keep it.
There was some talk over at Subguns awhile back about whether it was even worth the trouble to renew your license each time, or just let it expire and reapply since your books could start anew.