mmm, I love not being single
I'm not a rules-person. ok, so there are some common-sense things like don't call someone all day non stop, or don't just disappear etc, but in general I say call him when you feel like it. Ask him to hang out when you feel like it. Some people will now say "nooo if you ask him to hang out before so and so long, you'll look desperate" or whatever, but I don't think it matters, unless he is a very rule-aware person, that'll be the last thing on his mind. From what you've said I think he definitely likes you.
Oh, and just cos his friend didn't mention him mentioning you doesn't mean anything. Well, except that it tells me you're too shy to tell him how you feel and are in fact so shy you'd rather sneak around asking his friends. Me and my bf told each other we liked each other within a few days of first meeting each other.