7 or 14 days Pass

Hi,

I'm planning the following itinerary with my family:
D1 Ariport to Tokyo
D2-D4 Explore Tokyo
D5 Tokyo to Hakone
D6 Hakone to Kyoto
D7-D8 Explore Kyoto
D9 Kyoto - Osaka
D10-D11 explore Osaka
D12 Osaka - Tokyo
D13-D14 Explore Tokyo and fly back

1) I plan to take a 7 day JR Pass between D6 (Hakone to Kyoto) and D12 (Osaka - Tokyo). Is there any benefit for us taking a 14 day JR pass for the other trips (will be mainly in Tokyo)
2) is there a Shinkansen between Hakone and Kyoto?

Many thanks!