When you enter the underground lab, he flies out. Follow him and set down the mechanical mouse. He will eat it (chomp) and then follow you. You can use the owl to retrieve the fuel rod, by clicking on him and then on the rod.
There is no jail on Astro Knights Island. There is a castle dungeon, where an attacking alien robot is being held after his capture. (see the related question)
It is a mechanical mouse. (see related question)
You do not get or use a bucket on Astro Knights Island.
There is no treasure chest on Astro Knights Island.
Feed it the mechanical mouse (from the Maid's room) and the owl will follow you.
After you get the cheese you put it in the princesses dressing room and capture the mouse to feed it to the owl.
There are no bird eggs in astro knights island.
its on the island
To catch the mechanical mouse, in the Princess's Maid's room (castle first floor left).
How do you talk to the girl in the hay loft at astro knights island?
There is no Mechanical Island. However, Astro Knights Island is replete with robot plants and animals, while Steamworks island has actual plant monsters as well as mechanical devices. Game Show Island is populated by robots. (see the related questions)
In the Maid's room (castle first floor left) you will find a mechanical mouse.