Hi Suanz,
1. I reckon I should buy a one way ticket for Romance Car from Shinjuku to Hakone-Yumoto at 2280yen, and get a Fuji Hakone Pass from Odawara at 5650yen?
A: You are right.
2. However as the Fuji Hakone Pass is only valid for 3 days. Meaning I will pay for regular tickets for my 4th day. Correct?
A: It's correct.
3. Does Fuji Hakone Pass cover also cover limited express buses between Mishima-Gotemba-Kawaguchiko (operated by Fujikyu Bus)?
A: No. It covers between Gotemba-Kawaguchiko, by local bus only. Not covers between Mishima-Gotemba.
4. Is there any other cost-saving way I can go about this 5 day 4 night trip?
5. Lastly, to make my way from Kawaguchiko to Hakata, I should:
1) take bus from Kawaguchiko to Mishima
2) take shinkansen from Mishima to Shin-Kobe to Hakata
A: I think it's the cost-saving way with convenience.
1) buy one way ticket for Romancecar from Shinjuku to Odawara (1770Yen)
2) buy Fuji Hakone Pass at Odakyu sightseeing service center in "Odawara Station" (5650Yen) and go to Hakone-Gotemba-Kawaguchiko
3) take local bus from Kawaguchiko to Gotemba Station (1510Yen)
4) take the JR Gotemba line to Mishima (change trains at Numazu), and take Shinkansen
You can buy through fare ticket from Gotemba to Hakata with visiting Shin-Kobe at Gotemba Station, or use JR Pass.
About Gotemba Station,
https://en.wikipedia.org/wiki/Gotemba_Station
