Tokyo-Mt. Fuji-Osaka

Hi all :)

I'm planning to visit Japan in mid Nov to early Dec. Im coming from kansai airport then going to Tokyo for about 4 days with a day trip to mt fuji and then back to osaka/kyoto. I will be using a 7 day JR pass. I want to if,
1. Is it possible to squeeze in Hakone, Gotemba, Five fuji lakes, and a day trip onsen? My priorities are actually just seeing Mt fuji and go to an onsen called Yurari, then maybe some recommendations to make the day trip worthwhile.
2. Is it better to do Tokyo-mt fuji-osaka or tokyo-mt. Fuji-tokyo and then travel to osaka the next day. I'm thinking if i go straight to osaka and not come back to tokyo i'll be saving a night's worth of hotel in tokyo.