Japan in October 2023

Hello,
We are two people who are going to visit you awesome country starting:
October 8 (arriving at the airport and using JR pass to the Tokyo JR station) till October 12 - Tokyo October 12th we leave Tokyo and till October 17th will be in Osaka,
In between 14th from Osaka to Nara, On the 15th Osaka to Kyoto, on the 16th Osaka to Himeji / Kobe - all these two way trip On the 17th from Osaka to Hiroshima
On the 19th from Hiroshima to Tokyo
And on the 20th back to the airport.
My main questions would be:
1, If my calculations are correct, we would need a 14 day pass each ?
2. Confirm, if i am not mistaken, that all the places mentioned, can be reached with JR pass ?
3. Since we have three months, can we order the passes now and keep them save, until our travel ?

Thank you very much for your help here