1)For travelling on the buses within Nikko area which pass should one buy? The world heritage or all Nikko pass?

2)Is there a day pass available for unlimited travel on buses within Nikko area,
how much it costs? and
where can one buy it?

Certainly not the World Heritage or All Nikko pass, because you will be using the Japan Rail Pass to access Nikko. You could pay single fares. There also seems to exist a 1-day bus pass for Nikko and Okunikko, which pays off for a round trip to Chuzenjiko, but I am not able to find any details. It might have been discontinued. If not, you should be able to purchase it at Tobu Nikko Station.

Is there any discount for JR Pass holders on these bus fares?

The second one from the top (Chuzenji Onsen pass) covers the stretch from JR/Tobu Nikko station up to Chuzenji Lake (for \2,000), you can get on off anywhere within the area covered. One way ride up to Chuzenji Lake costs 1,000 yen if you buy a single ticket, so it makes sense to buy one :)
http://www.tobu-bus.com/pc/ticket/nikko.html
Unfortunately they do not seem to have English language page for this one.

You can buy it at Nikko station upon arrival.

Is Ryuzu falls covered under the 2,000 pass (for chuzenji)?

Also, there is another pass 2,650 yen on the website mentioned by MK - where does it cover additionally?

If you start early in the morning and travel at a fast pace, you can fit everything into a daytrip.

Is Ryuzu falls covered under the 2,000 pass (for chuzenji)?

No, it is beyond Chuzenjiko.

Also, there is another pass 2,650 yen on the website mentioned by MK - where does it cover additionally?