Hi,
If you are traveling at the end/start of the year, and you are sure of the trains you want to take, then reserving your seats ahead of time is a very smart thing to do. The end/start of the year is one of the busiest times to travel in Japan, and it will be harder to get seats.
You can reserve seats in any JR office. Someone in larger stations may be able to speak English at a very basic level. The truth is that few Japanese can speak English with ease. In school the goal is rote memorization and passing tests, not learning to communicate.
But that doesn't mean you are completely up the creek.
To reserve your seats, or if you get hopelessly lost, which is very easy in Japan, it is better to write out your questions in simple words. Japanese are still very poor at speaking English but are often glad to help you out. In case you don't know how to get back to your hotel, carrying a business card or matchbook with your hotel's address on it can also be a big help.
With regards to Mt. Fuji, it is a large volcano so it can't be "closed". But for climbing it the only safe times are July and August. At any rate, seeing Mt. Fuji from afar is much better than part way up it, where there is no real scenery or anything to do. Therefore, I'd suggest you go to either Hakone or the Fuji 5 Lakes Area. If the weather is good, you can have a grand view, but if not, there are still other things to see and do there. The JR Pass can only take you part way there though. So look into getting a Hakone Free Pass or a Fuji Hakone Pass.
In Tokyo a few of the best places to see are the Tsukiji Fish Market, plus the site that every last tourist goes to see, the Sensoji Temple. If you are in Tokyo on a Sunday afternoon, be sure to go visit Harajuku to see the youth with their wild fashions. Meiji Shrine and Yoyogi Park are next to it and well worth seeing also. And be sure not to miss the Shibuya Hachiko intersection especially on a weekend when it looks like half the city is crossing the street all together. The Sky Tree offers the best view over the city but it is rather pricey.
Visiting Nikko also makes a great day trip.
Going Tokyo-Osaka-Tokyo almost pays for a 7 day pass, but the difference you can cover quite easily with a side trip or two. Visiting Himeji near Kyoto to see Japan's best castle would do perfectly. Perhaps your next trip you can visit Kyoto and Nara as well - they are the crown jewels of Japanese culture.
A 14 day pass would not pay off without adding extensive travel; at the very least adding something like a side trip to Hiroshima.
Best of luck.
