7 days JR Pass Schedule - Itinerary - Please provide input - TIA.

We (family of 4) are in Japan for 10 days in October:

Day 1 - Fly into Haneda. Buy 3 days (72 hours) metro pass. Staying in Shinjuku
Day 2 - Tokyo sightseeing
Day 3 - Tokyo sightseeing
Day 4 - Activate 7 days JR pass. Train travel from Tokyo Station or Shingawa to Kyoto (Day 1 of JR 7 days JR Pass) - Night in Kyoto
Day 5 - Kyoto/Nara sightseeing (Day 2 of JR Pass) - Night in Kyoto
Day 6 - Train travel from Kyoto to Hiroshima, Miyajama (Day 3 of JR Pass) - Night in Miyajama
Day 7 - Train travel from Hiroshima to Osaka (Day 4 of JR Pass) - Night in Osaka
Day 8 - Osaka (Day 5 of JR Pass) - Night in Osaka
Day 9 - Osaka (Day 6 of JR Pass) - Night in Osaka
Day 10 - Osaka to Tokyo Narita (Day 7 of JR Pass) - Fly out of Narita

Thanks in advance and here are a couple of questions:
1) Does this itinerary look good and are we better of buying 7 days JR Pass vs buying separate tickets for each segment?
2) Will we have to pay extra for traveling on Shinkasen?

Thanks again :)