The windmill is at the far right side of the island. There are three areas : the Village, the Castle, and the Mill.
go pass the windmill and on the ladder is the rope.
The rope is on the water wheel on the right side of the windmill.
The attic of the windmill doesn't have a key, only an ingenious secret. (see the releated question)
Follow Don Quixote.
in the top of the windmill
you have to unlock the windmill
You do not get or use a bucket on Astro Knights Island.
Keep going to the right until you reach the windmill, which is the third section of the Island (the other two are the village and the castle).
There is no treasure chest on Astro Knights Island.
You use it to power the hover board (hovercraft) in the attic of the windmill. (see related question)
The mill gears on Astro Knights Island are in the second-floor loft of the mill, and they are locked to prevent the windmill arms from turning. Grab the short hanging rope to unlock the gears. Go outside and turn the windmill arms counter-clockwise by climbing on them, and you will see the roof dome open.
The spaceship in Astro knight is located in the mud next to the windmill