In combat the stars tell you how rare and how difficult an enemy is. Does that actually affect anything once I've captured it? Or is it only for your reference in combat? What does it mean! Thanks ^.^

EX: Does a 3 star pet have better stats than a 1 star. Or would an uncommon one have better stats than common?

Hi,
I know that uncommon pets usually have a visible trait such as wings or stripes or runes, and common ones don't. Sometimes a pet is said to be uncommon and it doesn't have any visible trait, in that case it carries the gene for it (but you won't know what gene until you've captured it and tested it). As for the difficulty level, I wouldn't know either because I'm new too. But here's one answer already :)

Number of stars doesn't raise the stats. But more, the harder, but the harder, usually the better equipment.

Color is just about genes of mutations. Common is none, uncommon is either a vis or carry, rare is I think two carries or two vis... I don't remember well since I've slacked off a bit from exploration. But there are a few guides out there that would explain it all. XD