purdue1015
1) Nozomi is a type of shinkansen train that operates on the Tokaido Shinkansen and Sanyo Shinkansen lines. Tokaido is a historical name, go learn about the Tokaido Road. San'yo is the name of a region on the Seto Nai Kai side of western Japan.

1.5) You can find out more on the web, subjects are Tokaido Shinkansen and Sanyo Shinkansen, and the three JR operating companies that you know about (there are three more).

2) You can look at the Kyoto- Shin Osaka- Miyajima- Hiroshima- Shin-Osaka to see if the Kansai-Hiroshima regional pass saves enough. And then add om a Shin-Osaka to Tokyo ticket. But this gets tricky because it is a JR West pass. No pass will do you any good for any of the Tokyo parts of your itinerary
JR Kansai Hiroshima Area Pass

3) The (nationwide) JR Pass options don't do you any good. Even if the regional pass saves a couple yen I would not do it. You just want to get on a shinkansen in Kyoto and get off in Hiroshima and, later, get on a Nozomi in Hiroshima and get off in Tokyo. That means just buy the tickets.

Maybe better yet: just fly from Hiroshima (HIJ) to Tokyo (HND). Even more better: you might find a carrier that would fly from HIJ to Narita (or maybe FUK->NRT).

4) yeah, pretty good

5) IDK