NRT to Tokyo: If you've got luggage and your hotel is served by Limousine Bus and the timing works out with your arrival, then to me it's almost a no-brainer to take the Limo Bus rather than the train to the hotel. In any case, it seems like you absolutely need to make the 21st (when you go from Kyoto to Narita) your last day of the 7-day JR pass, so you'll want to validate your 7-day JR Pass voucher on the 15th. So you really will not be able to use it on Mar 14th.
Imo, a dedicated trip just to go to the foot of Mt.Fuji's not worth squeezing into a fairly tight schedule like yours. On the other hand, you could make it more worth it by combining Mt.Fuji with something else. For example, take a trip to Hakone... on a clear day, you'll have a gorgeous fairly up-close view of Mt.Fuji from certain vantage points in Hakone. You could consider a lunch/onsen package at Hotel Green Plaza... hot spring while enjoying the view of Mt.Fuji followed by lunch buffet. They also have convenient guided bus day tours from Tokyo that include both Fuji and Hakone. Depending on the weather, you might be able to get a good view of Fuji from the right side of the bullet train while passing through Shizuoka on the way to Kyoto.