Tokyo-Osaka-Kyoto- Hakone/5 Lakes

Hi 👋

Just seeking your advice on using a JR pass for our trip in October this year. Our itinerary is as follows;

18/10-23/10 -Arrive at Narita airport at 7pm. Stay in Tokyo for 5 nights.
23/10-26/10 - Tokyo to Osaka. 3 nights Osaka.
26/10-29/09 - Osaka to Kyoto. 3 nights in Kyoto.
29/10-31/10 - Either Hakone or Fuji Five Lakes District.

Does the JR pass cover travel to either Hakone or the Five Lakes area?

We were thinking of taking a day trip to Nara. Is it best to get to Nara from Osaka or Kyoto? Does the JR pass cover the train trip to Nara?

On the 31/10 we would travel back to Tokyo. Then depart Narita airport at 8:30pm. Travel between Narita airport and Tokyo, what is the cost of the Narita express? Do you buy single use ticket or a return ticket?

Are we best to purchase our train travel tickets separately or purchase a JR pass? If a JR pass is more economical, do we get the 7 day pass, and at what point do we activate it to get the best use of the JR pass?

Thank you
Sarah and Bob