Need to buy JR 7 days pass?

Hello!

I was hoping you may help with my itinerary our family visit to Japan:

Day 1 Osaka arrive
Day 2 Osaka - Shinsaibashi-suji, Dontobori
Day 3 Osaka - Tsutenkaku, Shinsekai
Day 4 Stay at Kyoto - Gion, Hanamikoji
Day 5 Kyoto - Fushimi Inari- Taisha Shrine, Kiyomizu-dera temple
Day 6 Kyoto to Tokyo - Kaminarimon Gate, Ginza
Day 7 Shinjuku to Mount Fuji (round trip)
Day 8 Shinjuku to Disneyland
Day 9 Tokyo Shibuya
Day 10 Shinjuku to Haneda Airport

I have some questions:
1 - which rail pass should I purchase 7 days or other pass?
2 - would you suggest I purchase the green car vs economy class? We are traveling during early February.

Thank you so much in advance!