Train transfer to Otsuki

1.I'm using Kanto Pass to travel from Shin-Nihombashi to Kawaguchiko. On the hyperdia search show a few routes options.
Which station is easier to transfer between Kinshico or Shinjuku(JR) to take Ltd Exp Azusa?
Do I need to walk a distance to the platform or is just across the platform on the same level.
2. Is Suica/Pasmo card valid on bus to Kusatsu Onsen from Naganohara-Kusatsu terminal?
3. Is Yamanashi-Fuji and Holiday Rapid Mt Fuji part of JR which I can take using Kanto Pass?
4. Is Kanto Area Pass allow to ride on Tobu Line, Local or Ltd Express?.
Thank you.

Which station is easier to transfer between Kinshico or Shinjuku(JR) to take Ltd Exp Azusa?

Kinshicho would be easier (it is a much smaller station than Shinjuku), but there is just one train per day from Kinshicho.

Do I need to walk a distance to the platform or is just across the platform on the same level.

At Kinshicho you may not even have to change platforms. In Shinjuku you have to walk between platforms which can be quite far apart from each other. And the station is very busy during rush hours.

Is Suica/Pasmo card valid on bus to Kusatsu Onsen from Naganohara-Kusatsu terminal?

No.

Is Yamanashi-Fuji and Holiday Rapid Mt Fuji part of JR which I can take using Kanto Pass?

It is partially JR and partially Fujikyu, but the Kanto Rail Pass fully covers the train.

4. Is Kanto Area Pass allow to ride on Tobu Line, Local or Ltd Express?.

No. Except the JR/Tobu limited express trains between Shinjuku and the Nikko area and local Tobu trains between Nikko and Kinugawa. But the Tobu trains to/from Asakusa are not covered:
http://www.japan-guide.com/e/e2361_06.html

I'm using Kanto Pass to travel from Shin-Nihombashi to Kawaguchiko.
Which station is easier to transfer between Kinshico or Shinjuku(JR) to take Ltd. Exp. Azusa?

In Kinshicho (not "Kinshico") Station, as Uji says, you can get off a Rapid train and get on Limited Express Azusa 3 via the same platform. Then, you need to switch to a Fujikyu train in Otsuki Station.
Among Limited Express trains on Chuo Line, some "Azusa" trains skip Otsuki Station; "Kaiji" trains (running from Shinjuku) make a stop at Otsuki Station.

- Map of Kinshicho Station
http://www.jreast.co.jp/estation/stations/img/map/m_kinshityou.gif
: Eastbound Rapid trains (from Tokyo, Shin-Nihombashi, etc.) use Track 4.
: Westbound Rapid trains and Limited Express Azusa 3 use Track 3.
: Westbound Local trains (mostly continuing onto Chuo Line, for Nakano or Mitaka) use Track 1.

If you head to Kawaguchiko on a Saturday, a Sunday or a public holiday by November 2014,
you can take the westbound Rapid train departing at 10:05 from Shin-Nihombashi to Tokyo and switch to the Kawaguchiko-bound part of Narita Express 10 (departing at 10:21 and arriving at 12:43) via the same platform.
(Narita Express 10 is a two-destination train until Tokyo Station, where it is divided into two parts.)

Otherwise, to travel from Shin-Nihombashi via Tokyo to Shinjuku on two trains, you should make a long transfer in Tokyo Station from a Sobu Underground platform on the 5th basement to Chuo Line platform above the ground.
So, if you hope to catch a Limited Express train in Shinjuku Station, I recommend you take an eastbound Rapid train to Kinshicho Station, change platforms using elevators or escalators and take a westbound Local train. Then, in Ochanomizu Station you can switch to a Chuo Line Rapid train via the same platform.

Sobu Line has two ways in Tokyo Metropolis. Shin-Nihombashi Station is on its south way, which connects Tokyo Station and Kinshicho Station.
: Shinjuku --[Chuo Line]-- Ochanomizu --[Sobu Line]-- Kinshicho.
: Kurihama --[Yokosuka Line]-- Tokyo --[Sobu Line]-- Kinshicho.