Japan Rail Pass how many days

Greetings,

We are arriving in Japan on March 30th of 2026 and we are staying in Tokyo until April 2nd.
Then from April 2nd, we will be traveling to Hakone, Kyoto, Arashiyama, Nara, Kanazawa, Takayama, Shirakawa, Furukaya, Takayama and back to Tokyo. This itinerary will be from April 2nd to April 17th.

Based on this itinerary, should we buy the JRP for 14 days or 21days.
Once you buy and start to use the JRP pass, how the days are counted? Should I count April 2nd to April 16th, including weekends? or should I count only the days that I will be planning to use the JRP pass?

Based on my research, I buy the tickets online and then I need to pick up the tickets in one of the JRP offices? Please confirm.

thank you for your assistance
Emi