I saw that I can buy it at the Sightseeing Center at Asakura station, but it is only open from 8 to 2:30.I believe that the pass can also be purchased after 2:30 from the "Tobu Travel" travel agency, which is located inside Asakusa Station, but I am not 100% sure. Also, the office at Tokyo Station seems to be open until 7pm:
http://www.tobu.co.jp/foreign/news/20090826-1.html
I also saw that there is a JR "rapid" train to Nikko for about 1400 yen leaving hourly from 6:20 AM
No, there is no JR rapid train to Nikko. But Tobu rapid trains leave Asakusa Station hourly for Nikko. They are covered by the World Heritage pass. The basics are explained on the following two pages:
http://www.japan-guide.com/e/e3805.html
http://www.japan-guide.com/e/e2358_002.html