After a quick chat I've put my previous ideas together to create a puzzle style game which uses characters and there abilities to collect certain items, which you'll see in my brainstorms below.
The Witch's hiccups would be timed and depending on which colour hiccups come out, determines how long the light will be available for; some may hang onto objects leaving it behind as a permanent light source.
The Wizards sneezing would send him flying backgrounds, but you can save up his sneezes (you know when you sneeze but you don't? Then all of a sudden you sneeze 3 times in a row) to launch him further or not.
The Black Cat would be sneaky and be able to see in the dark, guiding you if the witch doesn't hiccup for a while.
Whereas the Frog can jump over objects in your way and even pull things towards you by using his elastic tongue like they do when catching flies.
The Broom is more of a vehicle for exploring, it can carry multiple characters but can't collect no items. It can be used to sweep items in certain directions.
The maze layouts you see aren't certain as it was just a way to show what was going through my head, but I have a vision in my head which would make the maze look like corridors in a house or something and there will be objects like tables etc.
The idea would be to get all the items back to the cauldron in order to move onto a different level, of which each would get more hard and complex as you climb the levels. Only certain characters can enter certain areas and you will have to find the other characters while searching the maze, starting off with the witch.
The witch doesn't have the ability to carry items as for as when she hiccups she jumps, dropping what she carries and the wizard is the same; except he'll drop them as he can't control himself flying backwards. The cat and frog can carry items a certain distance. But you can use the characters to push items depending on there ability.