I can see why you are confused.
The DIS website lists 6/24 as PM EMH, while allearsnet.com lists the same date as an AM EMH.
I checked the information with the Disney website and it was listed as 9am-11pm. Personally, I would go by what Disney says.
So, to answer your question, by going with the Disney times, the park would "close" at 11pm. This means that you need to get a bracelet for each member in your party if you would like to stay from 11pm-2am.
As for Epcot (and the other parks, as well), only certain rides and attractions are open during the EMH - not everything.
Here are the attractions open during Extra Magic Hours per the Disney website:
Magic Kingdom® Park
Mornings:
Buzz Lightyear's Space Ranger Spin, Cinderella's Golden Carrousel, Dumbo the Flying Elephant, "it's a small world", The Many Adventures of Winnie the Pooh, Mickey's PhilharMagic, Peter Pan's Flight, Space Mountain®, Stitch's Great Escape!, Tomorrowland® Indy Speedway
Evenings:
Includes attractions listed above and Big Thunder Mountain Railroad, The Haunted Mansion, The Magic Carpets of Aladdin, Pirates of the Caribbean, Splash Mountain®
Epcot®
Mornings:
Mission: SPACE®, Spaceship Earth, Universe of Energy, Test Track
Evenings:
Includes attractions listed above and Honey, I Shrunk the Audience, Journey Into Imagination with Figment, Mexico-El Río del Tiempo, Norway-Maelstrom
Disney-MGM Studios
Mornings:
Muppet Vision 3-D, Rock 'n' Roller Coaster® Starring Aerosmith, Star Tours, The Twilight Zone Tower of Terror
Evenings:
Includes attractions listed above and The Great Movie Ride, Playhouse Disney-Live on Stage!, Voyage of The Little Mermaid
Disney's Animal Kingdom® Theme Park
Mornings:
Discovery Island Trails (AM only), It's Tough to be a Bug!®, Kilimanjaro Safaris**, Pangani Forest Exploration Trail® (AM only)
Evenings:
Includes attractions listed above and The Boneyard®, DINOSAUR, Festival of the Lion King, Kali River Rapids, Primeval Whirl®, Tarzan Rocks!, TriceraTop Spin
Honestly, I can't recall about Epcot.
I hope the rest of the information will be helpful. Let me know if you have any other questions!
