The app shows up to April 30th, so you should start seeing your dates in the app calendar soon.
They are almost always on Monday and Wednesday. And usually Epcot Monday and Magic Kingdom on Wednesdays, though they can change both the date or the park occasionally. (MK is usually switched out to AK or HWS while Halloween/Christmas parties are running for example)
Expect them to be on May 4th at Epcot and May 6th at MK, but check the app over the next week or two until it is confirmed or if we see they made a change for those days.
Everyone who is going into the park will indeed need a form of admission, like an annual pass or a dated ticket, and it will use a day of your tickets to enter, even if it is only for the EEH event.