Both my current thralls use Fireball and it ends up hitting my companion or dog, and then the companion gets annoyed and starts attacking the thralls or the dog dies. I tried leaving their bodies in my house at Breezehome but they disappeared after a week and I will eventually want to use them again. So how do I keep their bodies their?

What i do is have my follower and dog wait outside any dungeon to guard the horse (lol) and just take the thrall in with me. Aoe magic will tick all other followers off to the point of killing them.

Unfortunately Skyrim is becoming one big "Escort Mission".

The best mage thralls are Ice mage variants (Cryomancers and the like). Most Ice spells have at worst minimal AOE ranges and hence minimal FF issues when compared to Lightning and especially Fire mages with their incessant Fireball spam all over the place. Of course it's slightly annoying that Ice magic is resisted by an awful lot of creatures/NPCs in this game but that's just the way it goes. Mage thralls are strong enough NPCs to power through those resistances for the most part in my experience.

Dont bring them.