22 days in Japan - 14-day rail pass

Hello!

I'm planning for a trip in March for 22 days approximately in Japan. Naturally looking forward to see as many things as possible, but also to immerse in the local culture. Can you let me know if my planned itinerary is good for the 14-day JR pass?

Days 1-2 : Stay in Tokyo
Day 3: Activate JR pass. Head to Matsumoto, stay there for a night.
Day 4: Head to Kanazawa, stay there for a night.
Day 5: Head to Shirakawago for day trip. (should I put up a night here to see the night lights? Or should I just head to Takayama in the evening?
Day 6: Stay in Takayama (hopefully a nice ryokan!)
Days 7-9: Head to Kyoto, stay for 3 nights
Day 10: Day trip to Hiroshima + Miyajima Island, then head to Osaka (or should I put up a night in Kyoto and head to Osaka only the next day?)
Day 11: Osaka
Day 12: Day trip to Shiga-ken (Lake Biwa and Omi beef!)
Day 13: Day trip to Nara
Days 14-15: Head to Hakone
Day 16: Head to Tokyo (Last day of JR pass)
Days 17-22: Stay in Tokyo and explore surrounding areas

Q1: Is the above cost effective for JR pass? From my research, all routes between cities should be covered by JR pass except for the Shirakawago day trip (will require a local bus, if I'm not mistaken).
Q2: Should I spend my JR pass trip to travel somewhere else instead of Hakone? Would it be expensive to go to travel between Hakone and Tokyo without a rail pass? We are not intending to visit/ climb Mt Fuji (not sure if it's open in March!), but would like to just enjoy Hakone as it is.
Q3: Are there many luggage lockers in the train stations?
Q4: Should I spend more time in Osaka or Kyoto? Currently I have quite a few days in Kyoto, not sure if I'd be too bored!

Thanks very much! :)