Do I need a JR pass and how many days would I need?

Hi,

A first time traveller to Japan. Just want to check whether getting a JR pass would be beneficial for my particular itinerary. And how many days would I need?

1. If I activate the JR pass at the airport, does that mean the days start counting then? Or only after I take the first trip?

2. Where can I activate the JR pass if I choose to not activate it straight after landing in Narita?

3. Please see below a rough layout of my 2018 trip:

15/11 - Tokyo
16/11 - Nakano
17/11 - Matsumoto & Narai juku
18/11 - Nagoya
19 to 26/11 - Kyoto, Osaka, Nara, Kobe
27/11 to 6/12 - head back to Tokyo for remainder of trip (perhaps Mt Fuji on the way back from Kyoto).

Hope to hear back from you soon and thank you in advance!