Leo is the equivalent of Interceptor in Final Fantasy 6.

Just in case the reference is lost on some, Interceptor was PC Shadow's dog, who would randomly jump in a fight and maul one enemy for you.
It really isnt the best analogy, since Shadow was suposed to be extremely competent

Leo's presence in the material world is derived from Lucy's magic. Otherwise he'd be slowly dying as he was when he lived without a summoner. Sure at one time he acted independently, but now he's basically one of her Pokemon. Only unlike the others he can leave his Pokeball at will which is damn handy since Lucy keeps losing her gorram keys.
And no, when Leo isnt summoned by Lucy then he isnt draining her magic, that was directly stated in the exam arc.
And yes, he might be slowly dying when he enters the world without a summoner, but so are we all, the only difference is that Leo can reverse the effect by returning home once in a while.

Right. Leo is Pikachu. Just being out of the pokeball doesn't separate him from the rest of the team.
Leo isnt Pikachu, he is much more sensible than his current owner, and does actualy have his own plans, agendas and desires.