Tokyo to Gotenba/Hakone

I will be going to Tokyo in Jun 2015 with my family. My itinerary is as follows :
1) 2 nights in Tokyo
2) 2 nights in Gotenba
3) Back to Tokyo

So we will spend 3days 2nights in Gotenba. We intend to visit Hakone, Gotenba Premium Outlet, and Mt Fuji (5th Station).
In Tokyo, we will be staying in Ueno station area.

Could like to check with you the following :

1) From Tokyo to Gotenba station, I understand that one can take the Romance Car, or the bus from Shinjuku. Which would you recommend?

2) There is a 3day Hakone Pass. I am thinking of buying this pass.
a) From what I read, this pass seems to only have the Romance Car option and not the bus from Shinjuku. Am I correct?
b) Can I buy this pass in the Japan Tourism Office in Singapore?
c) Can I book the seats in the Romance Car or Bus when I buy the pass in Singapore?
d) Where can I find the schedule for the Romance Car or the Bus?

Thanks for the help.

1)
If you purchase Hakone free pass(starts from shinjuku), you can get special discount on bus ticket, from Shinjuku to Gotemba (870 yen)
On the other hand, it cost about 3,000 yen to go Gotemba by Romance car so I think the bus is cheaper and suitable for you.

2)
a)As mentioned above, you can go Gotemba from Shinjuku by bus with additional 870 yen. However, as for Hakone, there is no way to go there except for train.

b & c)I'm not sure sorry...

d) You can find those timetable on Odakyu website.

I hope this reply will help you.

Stay Hakone(large onsen town) recommend and usual.

1)
Direct(no transfer) Romance car Asagiri operate numbers not a lot.
Bus,too depends on dep time.

2-d)
http://www.odakyu.jp/english/romancecar/timetable/c.html
http://www.premiumoutlets.co.jp/en/gotemba/access/bus/

I forgot to mention one important thing.

If you want to go Mt. Fuji as well as Hakone and Gotemba, Fuji Hakone free pass( 3day, 7400 yen) will be best.
With this pass, you can go above spot( Hakone free pass does not cover Fuji area.
For detailed information, serch Fuji Hakone free pass on website.

Thanks JPN & TIna for the help.

In summary,
a) Take a bus from Shinjuku to Gotemba station at 870 yen.
b) Buy the 3-day Fuji/Hakone pass to travel from Gotemba to
Hakone and Mt Fuji.

Do you know if I can purchase the 3-day Fuji Hakone pass in Shinjuku, or at the Gotemba station when I reach there?

Thanks.