Please help confirm the itinerary

Hello there. I'll be traveling with my family (two kids - 11 and 7) to Japan between the 30th of March and the 10th of April. Here is the itinerary I have put together.

A few questions:
1. If I start the JR Pass on Day 5 (day trip to Hakone), then I would end up needing 8 days of JR Pass. Does it make sense for me to do a day pass to Hakone without using the JR Pass?
2. If I start my JR Pass on Day 6 (travel from Hakone-Kyoto), will I be able to use my JR Pass for the rest of my itinerary mentioned below?
3. Will my JR Pass get me all the way to the airport?

Day 1 30-Mar Tokyo Harajuku and Shibuya
Day 2 31-Mar Tokyo Hamarikyu Gardens, Asakusa, Ueno, Tokyo Skytree
Day 3 01-Apr Tokyo Day Trip to Disney
Day 4 02-Apr Tokyo Day Trip to Odaiba
Day 5 03-Apr Hakone
Day 6 04-Apr Kyoto Ancient Eastern Kyoto
Day 7 05-Apr Kyoto Historic Western Kyoto
Day 8 06-Apr Kyoto Highlights of South and Central Kyoto
Day 9 07-Apr Kyoto Day Trip to Nara
Day 10 08-Apr Osaka
Day 11 09-Apr Osaka Day Trip to Hiroshima
Day 12 10-Apr - Travel back to Tokyo

Thanks in advance.

Regards
Parth