7 or 14 day rail pass?

Hello!

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

Day 1 Tokyo arrive
Day 2 Tokyo - Toyosu fish market, Team lab and Art aquarium Museum
Day 3 Tokyo - Ghibli museum, Sensoji temple
Day 4 Tokyo - Harajuku and Shibuya
Day 5 Hakone overnight
Day 6 Mt Fuji back to Tokyo
Day 7 Tokyo -->Kyoto
Day 8 Kyoto - Arishiyama Bamboo forest and manga museum
Day 9 Nara day trip
Day 10 Kyoto- Fushimi shrine and Nishiki food market
Day 11 Osaka day trip
Day 12 Kyoto-->Tokyo

I have some questions:
1 - which rail pass should I purchase 7 or 14 day?
2 - would you suggest I purchase the green car vs economy class? We are traveling during late March/April

Thank you so much in advance!