Kat - INFP
Bianca - ESFP
Patrick - INTJ
Cameron - ESTJ
Why do you think so?
Well, I'll admit to not much confidence in typing Cameron. His character just isn't that developed. He's not much more than a stereotypical nerdy-but-sweet protagonist, and we generally assume nerds are introverts, but he seemed to enjoy the company of others and we never really see him spending time alone, so I guessed E.
His plan for dating Bianca led me to the T and J guesses. It was pretty involved and seemed well-planned. The whole thing was just approached very rationally and logically. He didn't just ask her out. He schemed with someone else to get someone else to get someone else to put her in position to date, arranged background research, and signed up for her to be his tutor. I guess that's more J than T, but the whole thing seemed very reliant on logic, cause-and-effect.
I think N/S is very hard to judge for people/characters you don't know well, but Cameron didn't strike me as NT, so I went with S. I think the girls are much easier to type, and it looks like most of us agree on them.
Patrick definitely struck me as an introvert. He doesn't have a lot of friends, he doesn't want a lot of friends, and he seems content to spend free time by himself. He's capable of being charming, but he doesn't seem to like parties or big groups. His whole way of doing things is very off the beaten path, and he doesn't seem sensitive to other peoples' opinions. He's very creative and intuitive (off-the-wall ideas that always seem to be exactly the right thing to do, like "Can't Take My Eyes Off of You"). If you want to argue X/F rather than T, I'd accept that. I went with Thinking because he doesn't wear his heart on his sleeve and doesn't seem to care about hurting most people's feelings.
P/J, again, I don't feel strongly about. Certainly he does some things that suggest Perceiving dominance; he's very adaptive. I may have read too much into the whole "following a plan" bit, because half the time he just seems to show up and try to make the most of things. But all the background research on Kat, her favorite bands, etc., made me go with J. I wouldn't argue with X or P.
I see we had almost totally opposite profiles for the boys. What about you, why did you guess what you did?