1) Yes, no immigration.

2) Yes, NEX to Tokyo station, very long climb up to Shinkansen platform, as the NEX stops underground and Shinkansen leave from the top level.

3) The NEX runs twice an hour. Since the JR Pass does not cover the most frequent and fastest Nozomi trains, you'll have to take one of the two Hikari trains running every hour to Kyoto. Between 2 and 8PM, southbound Hikaris currently depart at :06 and :36 after the hour, arriving in Kyoto ~2:46 later.

4) No idea. Unless this is a Japanese holiday, there is no need to make such advance bookings. There are non-reserved cars if you just want to jump on a train.

5) The regular JR pass covers all of Japan. There are other region-specific JR passes (JR West, JR Kyushu) which are not big savings over the regular one.


I recommend:
1. exchange your JR Pass voucher for a pass at Narita
2. go to the ticket counter and get tickets all the way to Kyoto, including the connecting Hikari from Tokyo
3. if you get lost in Tokyo station and miss your Hikari, just get new tickets for the next one.