To defeat the rat:
Give it a bash.
Hit it with the iron bar.
To get to the island:
You can't get there for free.
Drop the gold coin by the boatman.
Is the picture any use?
Examine it for a magic word.
SHAZAAM will transport you.
What use is the wand?
It saves on building materials.
Wave it, in the right place, to create a bridge.
To cross the river:
Make a bridge of sorts.
Cut tree with axe.
To defeat Droolig:
A weapon is needed.
Hit him with the sword.
To complete the quest:
Use a magic word.
Use SHAZAAM in the Treasure Room.