Is cute the same as fajny/fajna?
No, it is not - fajny/fajna is like nice. We can call anything by fajny - fajny chlopak, fajny film, fajna muzyka, fajny samochod. Fajny chlopak is like a nice, cool guy.
In my view cute should only be used for kitties and puppies.
Well, I dont understand cute in that way, maybe I get it wrong, I dont know. But for me cute is when you see someone and you feel like to hug him or her, when you get that nice feeling inside, probably similar to the feeling when you see kitties or puppies. In polish cute is ładny, śliczny, milutki (or ładna, śliczna, milutka). But while guys get called milutki but ładny and śliczny is not that nice for them, I can imagine. Well, if someone likes boyish type or even childish type of a guy then it's fine. As for me I would call my boyfriend cute but I would not say he is śliczny or ładny, milutki is ok though.