I'm trying to figure out how to play this game. I've only been here a few days, but I'm getting stuck on Lost Grove, Dungeon of the Forsaken, and Arena. I tried getting 3 level 25 pets for the arena, but they just die horribly on the first 'easy' fight.

I have a team of 3 level 60+ pets I'm using for main game content, but it's getting too hard, and I don't know anything about breeding or raising stats (outside of proficiency bonuses). What I am supposed to do to get pets that wreck everything in battle?

Looking at your pets, I'd say issue 1 is with your lv.60+ pets' equips

Strength of non-grove equips is something like lv60 mythical > lv60 legendary > lv50 mythical > lv50 legendary > lv60 epic > lv45 legendary > lv50 epic > etc (I don't have lv55 equips to calculate for them, and I don't own any equips under epic quality that aren't from the grove) in terms of what gives the best stat boosts.

And yeah, the Grove is swarmed with nothing but lv65 opponents, not the most hospitable place for regular, not-stat-bred pets that aren't lv65 already (not to say they can't do it, but it's what one would call exceedingly difficult.)
(our team of 80-base-stat nytes got utterly obliterated by a wild 3-star Earth-element epic aurleon)

Anne has
lv60 Rare relic, lv60 epic armor, lv40 epic accessory, lv45 epic accessory

David has
lv55 Rare relic, lv60 epic armor, lv60 rare accessory, lv55 rare accessory

and
Laura has
lv60 epic relic, lv60 rare armor, lv55 rare accessory, lv60 rare accessory

So you might want to see about doing Dungeon of the Forsaken runs and sending pets on higher level Sanctuary of Saerielle Missions to try to get some Legendary and Mythical equipment for them

Also, grinding ore or two levels via DoF and in Astryl's Tanquility might help.

Can't speak for the Arena, we've never done anything with it.