Tokyo - Nagasaki - Tokyo

Hi, this is my route and dates-

Arrive Tokyo 21st April - 25th April (4 nights)
Hakone 25-27th April (2 nights)
Kyoto 27-1st May (2 nights)
Osaka 1-3rd May (2 nights)
Hiroshima 3-5th May (2 nights)
Fukuoka 5-7th May (2 nights)
Nagasaki 7-9th May (2 nights)
Tokyo 9-10th May (1 night)

I want to check that my JR pass can be used on all routes and that if I activate it on 25th April when I head to Hakone, does it finish at midnight on 8th May?

If so, whats the best way to get to Tokyo from Nagasaki on the 9th? Or is it better to head back to Tokyo on the 8th?

Thank you!!