Hey fellow New Yorker..
All the answers to your questions are posted on the
MNSSHP thread started by baloo.
I will answer the best I can, that thread is very long...
No you do not have to stay onsite, all you need to do is purchase separate tickets for the party, I wouln't wait too long to buy them, because they do sell out, even though you are not going on halloween, don't take a chance, I would reccommend you buy them prior.
Lastly, no park hoppers needed, just the special MNSHHP tickets, you can arrive as early as 4:00 and you will be given a wristband that will allow you to join the party. Once the park closes at 6:00 you will be directed to tommorrowland and will have to wait there from 6-7, so they can clear the park out. You can enjoy the rides in tomorrowland for that hour and at 7:00 the part starts.
I hope this helps, but you should really check out the thread, it is extremely informative. That's where I learned all of this.