Tokyo --> Kagoshima?

Hello. My family of 4 will be traveling in Japan for 13 days arriving in Tokyo hoping to stop in Kyoto, Hiroshima all the way south to my mother's home town of Kagoshima, maybe stopping in Fukuoka where I was born and then departing from Osaka.

My questions:

1) does a Jrail pass make sense for these destinations?
2) is there a high speed option in any of the trips between the cities I mentioned above that is included in the Jrail pass?
3) are there overnight train rides that we could sleep on?

I very much appreciate your expert guidance! It is my first trip with my family to Japan. Thank you.