Just a couple of items to discuss. When we visited Japan, we didn't have the chance to visit Nikko so I'm not familiar with the amount of time it takes to get there and back. We did visit the Mt. Fuji area and Hakone and it did take most of the day. Left early and got back around 10pm. Keep an eye out on the weather.. because I would not recommend going to Mount Fuji on a rainy or very overcast day, as these conditions don't make it easy to appreciate the scenery and majesty of Fuji. The day we visited, the skies were mostly cloudy and we didn't have the best of views of Fuji since it was mostly covered by clouds, and we were a bit disappointed by that.
Also, I am not familiar with the 1-way Suica N'EX pass you refer, but my understanding is that you can get a rechargeable Suica or Pasmo card upon arrival at Narita Airport and use it on the Keisei, JR lines and Metro (subway) system in Tokyo. Maybe getting a Suica or Pasmo card when you arrive and loading it with yen may make it easier for you to travel between train systems during your stay.
As for your last question, YES, you can use the single ride ticket to get you from Maihama to Shibuya as long as you ONLY use the JR trains. You can't use the JR single ticket if your travel plans include switching to the subway, Keio or Keisei lines. This is when a Suica or Pasmo card comes in handy as you can transfer between different train companies with ease. Hope that help.