Trains Covered by Japan Rail Pass and a general advise

Hello;

I'm planning to visit Japan in October and I would like to have an advice from you for the following:

• my trip plan to stay in Tokyo and then visit Osaka, Kyoto, and Tottori. is the following covered by Japan Rail Pass Ticket?

1) Tokyo (Shinjuku) - Kyoto.
2) Kyoto - Tottori
3) Tottori- Osaka
4) Osaka - Tokyo.
5) Shinjuku - Tochigi

• inside Tokyo; for example to go from Shinjuku to Asakusa & Tokyo Skytree and to Yoyogi Park and to Nezu Musuem and to Akihabara and also to Fuji mountain area; what is the best transportation method to be used? same in Kyoto, Osaka, and Tottori.

thank you in advance