Ideas for each theme

Platformer where player goes from left to right encountering strange goop which causes them to mutate in some way whenever they touch it. There will be several ways the player can change and each affects how they interact with the environment. The player may have to touch different things in the right
 order in order to solve a puzzle and complete the level.

Mr Fixit:
This is my favourite I think. The player is a businessman who fixes problems using buzzwords. You will have to complete a bunch of minigames which will reward you with tokens. These tokens will make up a final puzzle which you solve to complete the game.

Mysterious stranger:
Again, basic platformer, but with a story to it. The mysterious stranger pops up in random places to give you information. At the beginning you are just told to do what he says as you're in danger, but over the course of the game you slowly unravel a terrible conspiracy!

You are a spaceship captain, "The Negotiator". You "negotiate" dangerous obstacles to smuggle illegal goods from one place to another. You can also negotiate the amount of stuff you buy/sell at each checkpoint. Taking on more dangerous stuff means more  enemies after you. Each level there will be some mandatory stuff you have to take and the basic difficulty level will increase.

Critical hit:
RPG where everything you do destroys the enemy instantly. After a while everyone you interact with recognises you as the brutal murderer you are and avoids you. The player meets the families of the enemies they destroyed and is forced to think about what they have done. Then the player is arrested and goes to jail.