Family of 10

Hi,

I am travelling to Japan with a family of 10 (3 elderly senior citizens, 4 adults and 3 kids).

April 2 - Arrive in Tokyo
April 3-5 - Tokyo and all nearby local attractions (please suggest best means to travel around with Tokyo with a family of 10 including my 70 year old Dad)
April 6 - Fuji 5 lakes (Mount Fuji day trip)
April 7 - Tokyo to Osaka
April 8 - Osaka Local Siteseeing
April 9 - Day trip to Kyoto
April 10 - Osaka Local Siteseeing
April 11 - Day trip to Hiroshima
April 12 - Day trip to Nara
April 13 - Osaka to Narita
April 14 - Back to India

Q1. I am planning to purchase JR Pass from April 6 to April 13. Would that help?

Q2. What's the best means to transport luggage from Tokyo to Osaka and Osaka to Narita since I heard luggage is not allowed on the bullet trains?

Q3. My main worry is local travel within Tokyo, Osaka, Kyoto and Hiroshima. Kindly suggest if local metro (with/without pass) would be more beneficial or some 10 seater van would be more economical? I have not booked any such van so far though.

Thanks in advance for your advice.

Regards
Munish