I’m looking for video apps that can make you look like you are creating a tornado with your fingers or blowing colorful smoke, fire, or just something cool out of your mouth.
Any idea what software I should be looking for?
If you want a mobile application you are probably out of luck as most mobile devices don't have the computational power required. Otherwise you could take a look at Adobe After effect, wich is rather expensive, or Blender, which is rather hard to work with. For Blender there are a lot of tutorials and pre-made projects that could help you.