DO NOT get a 14 Day nationwide JR Pass.
Here's why:

KIX-OSAKA (about 3000 yen one way)

Osaka-Fukuoka (about 14,000 one way)
The Shinkansen Station in Fukuoka is Hakata Station the terminal of the Sanyo Shinkansen.

Fukuoka - hiroshima roundtrip by shinkansen (about 18,000yen)

Total: 35000yen

Cost of 14 day Nationwide JR Pass: 45100yen

Save: about 10000 yen by Not getting the 14 day pass.

Because your trips are spread apart and the Japan railpasses are only for consecutive days, I cannot suggest any passes for your long trips.

I would suggest purchasing your major train fares as individual tickets. With the exception of the Train from KIX-Shin-Osaka Station (for that purchase a one day 2000yen JR West Kansai Pass, it saves you about 1000yen than ifyou were to purchase the ticket individually).

You can purchase the JR West Kansai Area Pass at the Kansai JR Airport Station.

Btw we have an extenstive Japan forum here on Flyertalk
http://www.flyertalk.com/forum/forumdisplay.php?f=509

The direct train from Kansai Airport stops at Shin-Osaka Station and not Osaka Station, please refer to the directions from Shin-Osaka Station to Osaka Station mentioned by the OP or in the other thread.

The Shinkansen does not stop at Osaka Station as well, it stops at Shin-Osaka Station, so you'll have to make your way back to Shin-Osaka Station from Osaka Station, which isn't too hard as the stations are a short train ride apart.

I hope that information helps you.