7 days vs 14 days JR Pass

Hi,

Itinerary:

March 29-31 : Tokyo
April 1 : Osaka
April 2 : Nara
April 3 : Arashiyama
April 4 : Kyoto
April 5-8 : Tokyo

Will a 7-day JR Pass be sufficient for my traveling, or should I get a 14-day JR Pass vs cost effective?

If I go with a 7-day JR Pass, when should I activate it?

I read that a JR Pass is not accepted in the transport system of Tokyo, but what about in the other cities?

Will a JR Pass cover my travel from Narita Airport into Shinjuku?

If I don't reserved my seat in advance, is there a possibility that I won't get onto the train or I will just get a crappy seat?

Thank you in advance!