7 or 14 day pass?

Hello!

Pardon my ignorance, trying to determine if a JR pass suits us.

We arrive in Tokyo from Sydney on a Friday at 6.30am (Narita airport) - will we be able to activate our JR pass at that point (so early in the morning) and use it to get to Shibuya where we are staying for 6 nights?

Does the JR pass cover travel in Tokyo and day trips from Tokyo? Such as to zoos, museums and other central sights plus further afield day trips such as Mt Fuji.

Our itinerary is as follows

Day 1 - fly into Narita 6.30am then to Tokyo
Day 2 - Tokyo
Day 3 - Tokyo
Day 4 - Tokyo
Day 5 - Tokyo
Day 6 - Tokyo
Day 7 - train to Takayama (stay overnight)
Day 8 - leave Takayama to travel to Kyoto
Day 9 - Kyoto
Day 10 - Kyoto
Day 11 - Kyoto
Day 12 - return to Narita airport to fly home late that night.

Do we need a JR pass? Will it cover most of our travel, and should we opt a 14 day pass or 7 (activating the seven day pass when we leave Tokyo for Takayama?