Hi Koo,
This one is a little tricky, let's have a look at how much you would spend without the pass.
Kansai Airport--> ¥Osaka ¥ 1,160
Osaka Kyoto ¥ 1,080
Osaka Nara ¥ 1,660
Osaka Hiroshima ¥ 19,500
Osaka --> Tokyo ¥13,550
Tokyo -> Narita Airport ¥ 2,740
(note that so far I have left lake kawaguchi (or kawaguchiko) out, more on this below).
For a total of ¥ 39,690, this would not cover the price of a 14Day JR-Pass. A better option would be to get a 7-Day JR Pass and use it for mosty of your long distance travel, Hiroshima and Tokyo, together this is ¥ 33,050, the 7-day JR Pass costs ¥ 28,300 saving you at least .¥ 4,750. In addition you can either use it for your day trips from Osaka or travel on local JR-Lines Tokyo and perhaps use it for Kawaguchiko.
For Kawaguchiko, the hassle-free way to get here is from Tokyo, you can either take a JR-train to Otsuki and transfer there to the Odakyu Line to Kawaguchiko or take a HighWay bus directly from Shinjuku. A popular way is to set out by train and take the bus back to Tokyo. There is not much difference between both routes, the train can take a little longer because you have to transfer but you can save a couple of hundred yen because the first-part is covered by the JR-Pass. For the rest, I don't think you will need a Hakone Pass if you just visit Kawaguchiko, it is a great method to use when you plan on Exploring Hakone but a little pricey for just Fuji.
Let me know if you have more questions!
-Daniel