Should we get a JR pass?

Hello,

My brother is in Japan for work and we will be visiting 4/2-4/15. We will be staying at his Yokosuka apartment for the majority of the trip.

4/2 Narita to Tokyo, travel to Yokosuka
4/3 Explore Yokosuka
4/4 Tokyo for the day
4/5 Day trip to Miura peninsula
4/6 Day trip to Kamakura
4/7 Day trip to Hakone loop
4/8 Day trip to Yokohama
4/9 Travel to Shibu Onsen, stay in Shibu overnight
4/10 Visit Matsumoto on the way back to Yokosuka
4/11 Travel to Hiroshima, stay in Kyoto
4/12 Explore Kyoto
4/13 Visit Osaka on the way back to Yokosuka
4/14 Day trip to Tokyo
4/15 Tokyo/Departure

General questions:
I am seeing mixed information and from my tally it might be close. I am concerned we might have issues with the exchange pass. Will it be worth it to get a JR pass? Would we be able to do a 7day pass for the back half of our trip? I am not sure if the local trains/buses around Yokosuka are on the JR pass. Also, can we elect which 7 days we'd like to use the pass or is it for 7 consecutive days?

Thanks in advance!