The wall is only loose dirt. Keep pushing until it gives way.
Nothing. The wall is dirt and you can push right through it.
keep pushing it
walk through
You do not get or use a bucket on Astro Knights Island.
There is no treasure chest on Astro Knights Island.
you push through
When you get the moldy cheese from the castle dungeon, throw the wall switch that opens the rear gate to the cell. Later, you can enter through the tunnel from Mordred's lab.
You don't. Once you have gotten the cheese, and pulled the wall switch, that is all you can do there. You will have to enter the dungeon from Mordred's underground lab, through the tunnel he dug to escape. (see the related question)
There are no bird eggs in astro knights island.
In Mordred's underground lair, there is a way blocking the tunnel to the back of the dungeon. But it isn't rock, only dirt, and can be pushed through will a little effort.
its on the island
The wall to the left is just dirt, and you can push through it. At the end of the tunnel is the back gate to the dungeon (if you pulled the switch in the library, it's open). You will need Merlin the Owl to go with you. (see the related question)