Tokyo - Hakone - Kyoto - Tokyo

My partner and I are travelling to Japan next year, and I have a pretty good idea of where I want to go - I just need help confirming how to get everywhere!

We are staying for 7 nights - 8 days, here's the rough plan.

Day 1 - Arrive Tokyo @ night
Day 2 - Tokyo
Day 3 - Tokyo - Hakone (I'll buy the Hakone - but I think we'll catch the Romance Car there)
Day 4 - Hakone - Kyoto
Day 5 - Kyoto
Day 6 - Kyoto/Nara
Day 7 - Kyoto - Tokyo
Day 9 - Tokyo (depart)

So a few questions

1) Should I activate the JRPass when I arrive in Tokyo on the first day, or should I activate it on Day 2 so I can use it for the rest of my trip?

2) How useful is the JRPass getting around Tokyo for the day or two we'll be exploring

3) Is there somewhere I can confirm what stations I'll need to get to in order to go from Hakone to Kyoto, and then Kyoto back to Tokyo? I'll want to confirm what time we need to be at the station etc etc to use the JRpass

Any other hints would be appreciated.