[Elite Overlord LeSabre™]

Originally Posted by AmstroDamn

Does the pokemon's nature or even the other stuff like "happily eats anything" affects it's performance in battle?

Yes. Nature specifies a stat that will be higher than normal and one that will be weaker than normal (Atk +, Sp. Def - for instance) with the exception of five natures which won't affect stats at all. The "happily eats anything" refers to the Pokemon's Individual Value (IV) that is the highest. Unless you're breeding, you have little control over IV but you'd want to catch a Pokemon whose nature bolsters its strong points (a fast Pokemon with a Speed + nature, for instance).