Yeah, she's falling for him, and it isn't hard to see why
I'm really not sure if he knows who she is or not... If he doesn't (and that's the option I'm leaning towards), he might generally like her. Was/is he able to gain anything from being involved with her and the Utopium investigation she's involved in? I really don't know
It's strange, but very enjoyable
Though sooner or later Liv is gonna see them together, so that's another reason why I don't think Blaine knows who she is: otherwise he must've known Liv would be 'on to them' at some point.