Most of these questions can be answered from searching the forum.
But, in brief - no, you'll need to download it elsewhere (I strongly suspect). I haven't heard of anyone previously downloading it on their computers. (When I took the original
SCEA, I actually had to buy my voucher from Sun directly, rather than from Prometric.)
My understanding of the current requirements is that you have up to a year to submit your Part II assignment. (Which, IMHO, should be far more than enough time.)
You submit your completed assignment directly through the website, not via the
test center.