TiggerPiglet: The CMs have to attach the wristband to each qualifying Guest, so no, one person from your party can NOT get wristbands for the entire group. On the other hand, wristbands are distributed from about two hours before the EMH park closes to the general public until well into EMH night. So if your issue is that not all members of your party will be in the park before it closes, no problem.
izzys4: The parks aren't cleared out, but any Guest not wearing a wristband is NOT permitted to access any of the open attractions. They may or may not be permitted to stay in the park to shop or dine, but NO RIDES. Eventually, they clear themselves out.
DianeV: No wristbands in the morning. It's assumed that only (or primarily) Disney Resort Guests will be able to access the EMH park in the morning, mainly by using Disney transportation. What YOU will do is walk or - if it's running early enough - take the boat over to Epcot's International Gateway, enter the park, make your way as quickly as possible through World Showcase and start enjoying the open Future World attractions!