Itinerary Check Tokyo to Sapporo

Hello,

We are 4 adults going on a Japan trip.

We will arrive in Narita Airport on December 27 at 11:00AM; we're planning to get the JR 7-Day pass and would like to know if getting the pass is worth it.

From the airport, we would go directly to Noribetsu, we plan to stay 1 night there. After Noribetsu, we would go to Sapporo for 3 nights. One of those days, we would go on a daytrip to Otaru. From Sapporo, we would then go back to Tokyo on December 31. The following day after, we plan to go to Mt. Fuji and Gotemba.

My questions are:

1. Is the itinerary covered by JR Pass (Tokyo > Noribetsu ; Noribetsu > Sapporo ; Sapporo > Otaru and back ; Sapporo > Tokyo ; Shinjuku > Mt. Fuji ; Mt. Fuji > Gotemba ; Gotemba > Shinjuku)

2. May I know which rails to take for each one.

3. Is Mt. Fuji, Gotemba or places generally closed on January 1?

Thank you very much and hoping for your kind response regarding this matter.