Does Q love Picard? Yes, like a human could love a cat, or probably more accurataly, a pet amoeba. Still, it's love nonetheless.
In fact, it's clear to me that, beyond all the mocking and putting down, Q likes humans, and feels some kind of connection with them, and especially with Picard (who's the perfect "straight man" for his antics). In fact, I've long felt that he's kinda envious of the human condition, since in the show it's strongly suggested that humans are the new kids on the block, with a stellar but still largely untapped potential, while Q are more or less on a evolutionary dead-end, able to do almost anything but bored beyond recovery (something that is further explored in VOY even if with flawed results in my opinion).
As for Q being a villain, I don't think he's ever been portrayed as such, starting from Encounter at Fairpoint
. He puts obstacles in the way of our crew with the explicit purpose of having them overtaken by them. It's his way (cruel but effective) to teach humanity a lesson (this is extremely clear in Q Who
and All Good things...
, for example). To me, Q is far from being a villain: ironically, he could be humanity's best friend, guiding them to greatness. Our own "guardian devil".