Man you sound just like my friend, he was studying with this chick and having lunches and sh*t.
She bought him champagne for his bday too, although she didn't come to his bday.
He'd known her for a few months already and all I said to him was:
Ya gotta get off your arse and make a move cause friend zones are not a myth.
Also she might be just the bubbly and friendly type and you're reading too much into it ;)