Most economic JR Pass

Hi! We are planning on a trip to Japan on January 7-12

Itinerary
Haneda Airport —> Shinagawa, Tokyo
Shinagawa, Tokyo —> Niigata Niigata —> Sado Island
Sado Island —-> Kanazawa
Kanazawa ——-> Shinagawa, Tokyo
Shinagawa—-> Haneda Airport

Questions:
1. What is the most economical pass to use? JR NATIONWIDE PASS or JR EAST pass
2. If I will be using JR EAST pass, at what point from Sado Island to Kanazawa will it be NOT applicable?
3. Is JR EAST pass applicable from Haneda to Shinagawa and Shinagawa to Haneda?

Thank you so much for answering