The Minion I give to my Pet has any influence on my pets behavior? Battle Skill? Or any influence at all? Or it is just for my pet companion? What is exactly minions purpose? How shall I choose the minion for my pet?

Minions don't do anything other than keeping your pets happiness at maximum. It's useful if you have battle pets!

Zapping a pet with a minion can sometimes change the minion into another minion you can only get from the zapper.

There's currently a feature called the Minion Zoo where you can send minions and use them to fight, but it's in development atm and can only be accessed if you have a gold account.

Other than that, minions are just pretty things to have on the page as your pet's companion!

thank you so much! :D