- Tokyo Subway Route Map
http://www.tokyometro.jp/en/subwaymap/pdf/routemap_en.pdf[Transportation from Nikko to Hakone (Re: Questions 3, 4, 7)]
Unless you use Shinkansen (of JR-East / of JR-Central), your journey by rail from Nikko City to Hakone Town seems to require about 4 to 5 hours.
With an All Nikko Pass, you should start a trip by Tobu at Asakusa Station and finish it at either Tokyo Skytree Station or Asakusa Station.
: From these two Tobu stations, no train runs through to Odakyu Odawara Line.
I suggest you choose a Marugoto Nikko Tobu Free Pass instead. With this pass, you can start and finish a trip by Tobu at Kita-senju Station. This pass can be valid for 4 consecutive days, and the price is 4520 yen for a roundtrip from Kita-senju during April - November.
http://www.japan-guide.com/e/e2358_002.htmlChoosing this pass, you can take the following route.
{Part A: With a Marugoto Nikko Tobu Free Pass}
Tobu-nikko (07:41) --[Tobu: Section Rapid]-- (around 10:00) Kita-senju.
{Part B: With a subway ticket (240 yen per adult) and a Hakone Free Pass}
Kita-senju (C-18; around 10:20)
--[Tokyo Metro subway Chiyoda Line]--
(around 10:55; C-01) Yoyogi-uehara (around 11:00)
--[Odakyu: a train bound for Odawara or Fujisawa]--
(around 11:30) Machida (11:40)
--[Odakyu + Hakone Tozan Railway: Romancecar (additional 620 yen per adult)]--
(around 12:40) Hakone-Yumoto.
: In Kita-senju, your can exit Tobu through South Gate, purchase subway tickets, enter Tokyo Metro subway through the same gate, and go down to subway Chiyoda Line platform in the basement using escalators.
: In Yoyogi-uehara, Tokyo Metro subway Chiyoda Line and Odakyu Odawara Line are jointed.
: Paying 1340 or 1440 yen more per adult, you can leave Tobu-nikko about 1 hour later, take a Ltd. Exp. Kinu from Shimo-imaichi to Kita-senju and reach Hakone-Yumoto about half an hour later.
A major difference between an All Nikko Pass and a Marugoto Nikko Tobu Free Pass is that the former pass can cover Shimo-imaichi -- Kinugawa Onsen -- Shin-Fujiwara while the latter does not. You do not plan to visit Kinugawa area, so I suppose the latter pass is enough.
Regarding Romancecar, I suppose it is worth checking whether you can reserve your seats, pay for Ltd. Express charge on credit and print out your tickets through the website.
http://www.odakyu.jp/english/romancecar/e_romancecar/howto.htmlI recommend you get Hakone Free Passes and Romancecar tickets soon after arriving from NRT to Tokyo, for example at a counter of a major tourist agency.
[Transportation in and around Tokyo (Re: Question 7)]
Toei and Tokyo Metro One-Day Economy Pass (1000 yen) You can choose a 1-day Tokyo Subway Ticket, which will soon become available on the next Monday for 800 yen.
http://www.japan-guide.com/e/e2017.html[Accommodation in Tokyo (Re: Questions 2, 5)]
In Kita-senju, you can make a transfer among
Tobu (Isesaki Line, partly nicknamed Tobu Skytree Line),
Tokyo Metro subway (Chiyoda Line (C-18) / Hibiya Line (H-21))
and JR (Joban Line).
The area around Ikebukuro Stations of JR and of Tokyo Metro subway (Y-09 / F-09 /M-25), which is accessible by Narita Express, sounds nice for you to stay.
Starting from Ikebukuro of JR, you can use JR Yamanote Linefs outer loop to Nippori then JR Joban Line to Kita-Senju. In Nippori, you can switch to Keisei Main Line via one transfer gate and take a non-Skyliner train bound for NRT.
: JTB, Kinki Nippon Tourist and H. I. S. have branch offices near East Entrance of Ikebukuro Station of JR, which are open not only on weekdays but also in weekends.