Pets would be great if they worked like below
New Skill - Beast Mastery!
Skill Information - This skill allows you to train beasts to do as you command, this skill is put under the personality attribute.
Pets...
They should be normal companions. And if they should die, just use your Beast Mastery skill to try to tame it (100 skill would equal 100% chance with all lesser beasts (wolves, rats, etc.), and about 25% with greater beasts (bears, etc.) and if you fail, you cannot try to tame that type of beast for at least 24 hours. The pets should fight for you and thats it, no fetch, no digging up treasure, just fight.
Oh please no! I mean, I understand that TES was built from D&D blocks, but if this is fun for you, why don't you go play with a spreadsheet editor or something? There was a reason, why Bethesda abandoned exp based skill system and part of it is definitely the amount of calculation that takes place in games that have it. Stuff like that breaks immersion. Besides, what you described is, by far, not a normal companion, rather a summon and we already have those...