travel btw Tokyo and osaka

Hi, we're planning to travel to japan in oct for 12 days. We are flying in to tokyo and departing from osaka. We bought a 7 day jr rail pass and want to make the most of its use. I have several questions....
1. Should we go frkm tokyo > kyoto > hakone or tokyo > hakone > kyoto?
2. We plan to spend one night in hakone and want to see mt fuji and go up the hakone ropeway. Should we buy a fuji-hakone pass or hakone free pass or will jr rail pass cover sightseeing in hakone area?
3. While staying in osaka, plan to do daytrips to nara and hiroshima Are there any other short day trips that are recommended?
Thank you so much