1)
It will take about 60min by trains, but with transfer 1 or 2 times.
https://goo.gl/maps/cuwHe3aXbJsAnd if the airplane is delayed, taxi fare costs about 10000Y, it is waste.
So change the hotel to not so far location fr HND.
(If you do not exchange to Japanese money "YEN" yet, you cannot purchase a ticket of train.)
2)
It depends on your age and what you want to eat.
Popular Ramen(noodle) shops etc, have to wait, but fast food shops are not.
And if possible, eat breakfast you can buy it at near convenience store.
3)
The transportation network in Tokyo is very complicated.
It is impossible to memorize all of rail map, name of lines and stations,
so please check in advance as much as possible at Google MAP.
4)
Do you want to go exact location of Mt. Fuji?
Although it is understood that it does not go to the top of the mountain,
please check the size of Mt. Fuji again by seeing the map first.
If just want to see it, you can see even from the observatory space in mid Tokyo .
If really want to go nearby, "Lake Kawaguchi" on North or "Hakone" on South usual.
You will definitely despair of your roughly planning, if this goes on.
Ton of same Q posted here already, read all.
http://lh3.ggpht.com/-dmiN1c2Vat0/UhAmhVAlmvI/AAAAAAAALlk/TRLRJQm6lao/...