Minecraft Forge lists you all mods in minecraft and Forge

The Vanilla version of Minecraft refers to the game with no mods or texture packs installed.

Nothing will happen if you keep installing and uninstalling Minecraft. Minecraft does not track how many times you have installed it nor does track how many computers you have it installed on. The only drawback is if you uninstall Minecraft by deleting the .minecraft folder you will lose all of your saved worlds on that computer.

You may not have installed it correctly. Just reinstall.

That will usually happen when

a) Your Java has a problem

b) A Minecraft Mod was installed incorrectly

c) The files of your Minecraft is messed up