Last day of JR pass

Hi,
I'm currently traveling in Japan and wish to know about the validity of the JR pass on last day.
However, the staff here seems to have problem on English communication so I have to ask here =(
On my 7th day of jr pass (7 day pass), I reserved a ticket of hamanasu overnight train from Sapporo to Aomori, which will reach Aomori about 6am in the morning, however I wish to travel to Tokyo using Hayabusa Shinkansen, and I know also the JR pass will cover the basic fare before first gate you exit, and here is the problem:

1. To get on the Shinkansen in Shin-Aomori , I have to go through the Shinkansen special gate, is that counted as exiting the gate? Will the person let me in?
2. If I pay for 指定席料金 (since hayabusa is all reserved seat) can I travel safe from Shin-Aomori to Tokyo ?
3. What should I do if the person in Tokyo Station stop me while trying to exit the gate(if the above methods working) Please write me some japanese explanation if possible so I can show it when needed.

Please help it's in urgent! Thanks a lot!