Sounds like a great trip! Here are some answers:
Does it include a Ferry crossing to S. Korea ?
No - the Japan Rail Pass does not cover the ferry crossing to S. Korea
If I start my journey in Osaka how can I best use my JR pass to visit Hiroshima, Nagasaki, Kyoto,
Tokyo, Mt. Fuji? Can u suggest a 7 day route plan?
I think as you're going to travel from Hakata to Busan (I think), then you'll be best to end your rail travel in Kyushu. This means that the best approach will be to travel up to Tokyo on arrival, and then gradually travel down the country, stopping at all your itinerary locations en route. I have assumed you intend to visit Hakone for viewing Mt Fuji and have the following route plan:
- Kansai airport > Tokyo: ¥15630, (264mins, 613km)
- Tokyo > Odawara: ¥3640, (35mins, 83km)
- Odawara > Kyoto: ¥11750, (160mins, 429km)
- Kyoto > Osaka: ¥1680, (27mins, 42km)
- Osaka > Hiroshima: ¥9950, (108mins, 345km)
- Hiroshima > Nagasaki: ¥9950, (108mins, 345km)
- Nagasaki > Hakata: ¥9950, (108mins, 345km)
TOTAL: ¥62550 for 7 legs
Therefore, with a 7 day rail pass (¥28,300) you'll make a saving of at least ¥34,250 over individual tickets. By following the route I lay out above, aside from the initial hop up to Tokyo, you'll keep your journey times between cities to a minimum, and maximise your time exploring Japan.
For Hakone you should travel to Odawara with the JR Pass and from there purchase the Odakyu Hakone Freepass which will give you free travel up to and around the lakes on all the rail, funicular and cable cars that travel around the area. You can read more about the Odakyu Hakone Freepass online.
While you are in Tokyo you can also use the Japan Rail Pass on all JR trains in Tokyo. (Here's a map of JR lines in Tokyo for reference).
As an extra tip, you mention that you'll have to travel back up to Osaka from Hakata once you return from S. Korea. A 7 day rail pass is ¥28,300 and a 14 day rail pass is ¥45,100 with a difference in price of ¥16,800. The ticket price of the trip from Hakata to Kansai Airport is ¥15,840 (itinerary), so if you think you need a little more flexibility (eg, 8 days in Japan rather than 7), then you could opt for a 14 day Japan Rail Pass with only a ¥960 difference in the overall price of your rail travel.
You can look up train timetables and costs at the hyperdia travel planning website and learn how to use Hyperdia for Japan Rail Pass holders through our video blog.
Hope this helps!