"Is counter-transference normal?" Absolutely

"Like transference is normal? I mean, it just means feelings for another person, right?" Yes and yes.

I think such feelings are not just 'normal' but... necessary? expected? Because human beings are wired to feel in interaction with any other human being (be it T, a friend, the mailman). So, it is not so much holding such feelings (e.g. transference or counter-transference) that is problematic but what someone does with having such feelings.

Some Ts deal with it well.. Some deal with it poorly and/or mess up big time.