Value of JR

Itinerary in Oct:
Tokyo - 4 full days
Day tip to Kamakura (day 3 - activate pass)
Day trip to Nikko
Train to Kyoto and 11 days in Kyoto
Day trips to Osaka, Nara, Himeji, Hiroshima, Koyasan
Train to Narita
I have looked on multiple sites for the value of the JR Pass and it seems of value however - thinking 14 days (green class)
Questions: are my calculations correct?
Can I book a the major legs of my trip 1 month before I go and when I arrive in Japan pick up the tickets?
Where can I find the timetables to work out the day trips (times to leave and return … for example Hiroshima return as it will be a long day.
Thank you