The JR passes offer HUGE savings if used properly. Maybe for around Tokyo excursions the three-day Tokyo-wide pass might suit for some day-trips. For a short trip (like to Fuji) the 7-day National pass is completely the wrong tool for the job - ordinary train tickets are more appropriate.

Yes, buy Paso card, as follows, when you take Keisei Skyliner Express from Keisei Narita Airport station to Keisei Ueno station.

https://www.youtube.com/watch?v=YS38u1HHzxE

You should go to Lake Kawaguchiko to see Mt. Fuji by a highway bus from the Express Bus Terminal (BUSTA) in front of the South Exit of JR Shinjuku Station. It takes only 1,750 yen and @2 hours oneway. It's good to stay one night at an Onsen Ryokan there as follows.

https://www.tripadvisor.jp/ShowUserReviews-g1165976-d1412188-r369738647-Toki_Yuyu_Rakuyu-Fujikawaguchiko_machi_Minamitsuru_gun_Yamanashi_Prefecture_Chu.html

You can get either card at many train stations or just get at the airport before going to the city.

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