In English, thinking of the girl and thinking about the girl have two different connotations. The former implies that the boy is keeping her in mind when making a decision or doing something, while the other implies that he is just thinking about her in general. Which is the case here, and is there a way to tell them apart?
"Tror" = believes.
"Synes" = is of the opinion that. Used of subjective matters. "I think this film is too long". "I think this pasta is too hot". The speaker knows that there is no matter of fact.
"Tenker på" = ponders, reflects on. Plain "tenker" without the "på" means to conduct the activity of thinking. Eg: "Think before you speak", "He thinks in dollars and cents", "She thinks in picture".