Unity game engine
 

Is there any alternative to the Unity Game engine or can I run it On Linux????

Linux support for the Unity engine is currently in beta phase.
Alternatively you can try Blender's game engine.

I am planning to play "Cartoon Network: Fusion Fall" will it work with Blender??

A game only works on the engine it is written for, so no, it most likely will not run with blender. I assumed that you want to write a game, not play a game.