12 Days Trip

Hi my trip is already planned and it will be 12 days in total with 6 days in Osaka and remaining 6 days in Tokyo.
Itinerary will be Narita > Osaka (3 days) > Kyoto (3 days) >Tokyo (Shinjuku) > Narita Airport.
Give that I am going for 12 days, I guess 7 days pass will be ideal and planning to activate on Day 1 to travel to Osaka from Narita and Day 7 from Osaka to Tokyo. My qns will be:

• Can it be used from Osaka to kyoto?
• Can it also be used to travel to Nara?
• For last day, what will be the best way to get from Shinjuku to Narita Airport?
• Is there a way to purchase airport express ticket?

Thanks!