Maximizing use of 14-day Pass

We have family of 5 traveling at end of May for 16 total days.
We have 3 primary questions we're looking for feedback/advice on how to best use the JR pass:

1) Given the 16-day trip, when should we activate the 14-day JR Pass, and go single-purchase passes or use other transit for remaining days, etc.? Our itinerary is as follows:
Day 1 - 5: Arrive in Haneda, travel from airport to hotel, and then sight-seeing in Tokyo
Day 6 - 9: Travel to Kyoto and sight-seeing in Kyoto
Day 10: Travel to Nara, then on to Osaka
Day 11-12: Sight-seeing in Osaka
Day 13-15: Travel to Tokyo Disney (possibly via Hakone), tour Tokyo Disney
Day 16: Travel from hotel at Tokyo Disney to Haneda for departure
We're assuming we start the 14-days on Day 1, and book single rail pass (or use taxi) to go from Tokyo Disney to airport for final departure on Day 16...but would appreciate your thoughts.

2) Will the JR Pass work well for sight-seeing in the major cities (i.e., Tokyo, Kyoto, Osaka), or will we still need to buy local/regional passes when traveling throughout these cities?

3) Is Green/First class easy to use/book for the daily trips in the cities, or is it really only practical for the long-trips (Tokyo-Kyoto, Kyoto-Nara-Osaka, Osaka-Tokyo Disney)? Is it even possible to upgrade select trips/routes from Ordinary to Green class, or do we need to buy all Ordinary or all Green class for the full 14-days? If all the same class, is it easier to make reservations in Green/First class vs. Ordinary/Standard class (i.e., more availability) or are there fewer seats and more difficult to find 5 seats together, etc.?

Thank you in advance for your help and guidance. We very much appreciate it!
Todd