Hi there!
You can use the JR Pass for all of your planned travel, you can reach both Yokohama and Kyoto with the Shinkansen. Mt. Fuji can also be accessed with the JR Pass, however it does depend on where exactly around Fuji you wish to visit, sometimes an extra fare is required when traveling requires companies other than JR. However even then savings are to be had!
A 7 day JR Pass is roughly the same price as a normal return ticket Tokyo - Kyoto on the Shinkansen, this means that any other travel you do after is basically what you save. Given that a return Tokyo - Kyoto is on your list, I would certainly recommend a JR Pass.
As for Shinkansen travel, the Shinkansen is the name for the high speed bullet rail between various cities in Japan and different types of trains travel on the Shinkansen. For instance between Tokyo and Kyoto there's the Nozomi, Hikari and Kodama. The JR Pass does not include travel on the Nozomi but does cover travel on the Hikari and Kodama trains. The main difference is that the Nozomi only stops at a limited amount of stations (and thus is faster if you travel between these stations), the Hikari makes a couple more stops and the Kodama stops at every Shinkansen station. This may sound like a lot but it is generally something which you don't have to worry about when you use the JR Pass. This is because the JR Staff will always find the right trains/route for you when making ticket reservations, you just tell them where you wish to go.
I hope this helps!
Daniel
