JR 7-Day Pass

Hello,

I will be traveling to Japan for 8 nights

Haneda Airport - Tokyo (4 nights)
Tokyo - Kyoto (3 nights)
Kyoto - Tokyo (1 night)

1. Should I get the 7 day or 14 day pass?
2. If I buy the 7 day pass, when should I activate?
3. If I activate starting the day I will travel to Kyoto, how can I get from Haneda to my hotel in Tokyo? Do I pay for a separate ticket?
4. If I will be visiting Mt Fuji, Hakone, Disney while staying in Tokyo, should I activate JR pass for that?

Thanks in advance.