Now, I may have my information wrong, but I believe that when there are Extra Magic Hours (EMH) there is no opening ceremony. Now I may be wrong. There may be an opening ceremony and it just isn't covered by my department on EMH days.
When cast members lead the way, walking with the rope at their own pace.
Epcot has a very small opening ceremony, involving some characters, and the Test Track car. It takes place after they open the turnstyles and allow you into the Innoventions area.
A walk-back is like a rope-drop, but without a rope. A group of CMs line up and walk in front of the mob in order to keep people from running to the most popular attractions. At one point, the walk-back was to MS and TT. Now it's to Soarin'.
Yes they do (or they did) - I saw it last August - ok, so its not as grand as MK or AK but there was a countdown and a rope drop - followed by the escorted walk across to Soarin'