[Rogozhin]

I don't know about the metro pass (I'll hazard a guess and say it's only valid on the day you take the limo bus) but with the JR pass, you can exchange your voucher for one at Shinjuku station (it's an easy process as well, provided you have the necessary ID/documentation). You can make reservations but you don't have to, you can freely go in and out of the gates with the pass and take any available unreserved seat (not Green or on Nozomi however, I assume you have an ordinary ticket). You can't take the shinkansen directly from Shinjuku, but you can use your pass to get to Ueno, Shinagawa or Tokyo on the JR Yamanote line and take the shink from there.

I had my pass activated in advance (I went the day before to the JR exchange office and had it activated for use starting from the next day.) This could be a good option if you don't want the hassle on the same day as you start your journey.