7 or 14 days pass

Hi, happy new year! We are a family of 4 and planning a 15 days’ trip to Japan this summer. Our tentative itinerary is as follows:

Day 1 Arrival at Haneda airport - Overnight in Tokyo
Day 2 & 3 Tokyo sightseeing
Day 4 Trip to Nikko and back to Tokyo
Day 5 Tokyo to Hakone
Day 6 Hakone to Kanazawa (2 nights stay at Kanazawa)
Day 7 Kanazawa sight seeing
Day 8 Kanazawa to Takayama (2nights stay at Takayama)
Day 9 Takayama sight seeing
Day 10 Takayama to Kyoto (3nights stay at Kyoto)
Day 11 &12 Kyoto sightseeing
Day 13 Kyoto to Hiroshima to Miyajima
Day 14 Hiroshima to Osaka
Day 15 Osaka to Tokyo for flight back home.

In respect of the above, I have the following questions:

1. I was thinking of buying 14 days’ JR Pass. Hope it’s the one which should be preferred unless you suggest otherwise.
2. Would JR pass cover all the aforesaid journeys?
3. Would internal commuting within cities like Tokyo, Kyoto, Osaka, Takayama or Kanazawa be covered by JR pass? I tried to find relevant information but couldn’t find all. For instance, I could gather Yamanote line is covered but couldn’t understand about coverage of Metropolitan line by JR Pass. Your guidance in this regard will be appreciated.
4. If internal travel within these cities is not covered by JR pass, do you suggest buying any other pass for these cities or should I buy tickets on the go? Can I use any buses in these cities which may be covered by JR Pass?

Looking forward to your response. Thanks