The Fairy Park will show up during short periods of time. You could check the countdown in the widget on the right side of the playing screen that will appear some hours before the challenge starts. 
You will get special statues for your permanent parks (also for the upcoming ones) depending on your result. They will decorate your park entrance, will provide new boosters to your rides, and will increase entry fees.
In-app event boosters are different from the purchases in your regular parks because they are designed for event mechanics, but the no-ads offer will also work during the event.
Since the event will provide new boosters each time, the park will restart every week so you could accomplish all the challenges requested.