re: extra day. Besides d’rabanan, we got tradition of doing 2 days after Samaritans interrupted fire signals towards Bavel by creating false fires. By Hanuka, Samaritans were, as Jews, affected by Hellenism, then were defeated by Hashmonaim, so had probably less time to play with fire. Also, they might not have cared about Chanukah that was not their holiday.
Also, you have 25 days to reach Bavel, more than usual 14.