Most 3 day or more park hoppers come with one day of EE. For the last year or so, they have been offering onsite guests EE on each day it is offered during your stay. That could end at any time, but there are no rumors that it will be. If you are staying in the next couple months you should be fine. You'll need your room charge slip to prove you are staying onsite. If you try to call and ask about this special, they will more then likely tell you No, its not offered. They like to tell you about it at check in to make it feel really special. LOL
EE is currently offered on Mon, Tues, Thur and Sat. Its one hour before park opening. Fantasyland is the official land that is open. Most of Tomorrow land will be open as well. You can not get fast pass until park opening time.
Hope that answers all the questions, plus some!