JR Pass 7 or 14

Thank you in advance for answering my question.

Traveling from US to Japan
Day 1 - Arrive in Narita Airport take train to Kyoto
Day 2 - Stay in Kyoto
Day 3 - Day trip from Kyoto to Osaka back to Kyoto
Day 4 - Day trip from Kyoto to Nara back to Kyoto
Day 5 - Stay in Kyoto
Day 6 - From Kyoto to Tokyo
Day 7 - Stay in Tokyo
Day 8 - From Tokyo to Narita airport

(1) Should I purchase JR Pass 7 and then single ticket for my 8th day or purchase the 14 days?

(2) Can I use JR Pass from Kyoto to Nara?

Thank you.