If your pet is like, dying basically, will it affect it in any way?

Like, if it's hunger and happiness is all the way down in the red. Complete red.

No. The only thing that happens is that they can't battle.

Oh, okay. Thanks C:

there's a resort in Veta Lake that will feed your pets cheaply, and adding even the most common minion will make your pet happier. (This makes Major Drills harder to do, if you want to do those quests)