JR Pass for Holiday Rapid Mt Fuji

Hi, I searched on Hyperdia for routes to Kawaguchiko from Shinjuku and found the following two JR trains:
1. Holiday Rapid Mt Fuji 1
2. Yamanashi-Fuji 3

It appears that these 2 trains travel directly from Shinjuku to Kawaguchiko.

Will my JR pass cover the entire trip for these trains?

Probably not, since the train runs on non-JR tracks for part of the trip, so you will probably have to pay the fare for the corresponding section, as is usual for JR trains running on non-JR tracks.

Will my JR pass cover the entire trip for these trains?

No, the nationwide pass does not cover the Fujikyu Railway, however the Kanto Area Pass does.

http://www.japan-guide.com/e/e2361_06.html

Probably not, since the train runs on non-JR tracks for part of the trip, so you will probably have to pay the fare for the corresponding section, as is usual for JR trains running on non-JR tracks.

How can I find out the price that I need to pay for then?

It's the regular fare on the section between Otsuki and Kawaguchiko (1140 yen), plus I think you might also have to pay the 300 yen limited express fee.

Is it possible to pay the non-JR fee beforehand in Shinjuku? I heard it is possible to pay it at a JR office? Also are JR pass users able to reserve a seat on this for free?