Where can I find wild pets with traits? Also, is there like a map that shows which wild pets are where?

what you will want is, in face, our field guide to sylestian fauna, specifically this post, (although it is minorly outdated in some small ways, but those ways aren't relevant unless it's sprinfest or you're up to the very last section of the game, the lost grove temple)

(there's also a post about what the star colours/rarities mean earlier in the thread, post3)

But you can actually find 1v pets anywhere in the game, they're just less common in the viridian meadows area compared to the later areas (and of course pets that could be 1v aren't guaranteed- blue-star rarity pets can also be 2c)

Thank you so much!