Dorm life depends on which dorm you are placed in. The freshmen high-rises (Morrison, Ehringhaus, Craige, and Hinton James) are very social, with suites of 6-8 students. The hall-style dorms vary depending on the people on the hall. I had a hall-style dorm my sophomore year, and I didn't like how quiet it was and the fact that I didn't get to know many people on my hall. However, on one of my best friend's hall, they all went out to dinner all the time and played games together and joined intramural teams together. So it really just depends. It's your job to be proactive about being social.
Men's basketball is by far the most popular sport on campus. Getting tickets to games is decided by a student lottery, and more often than not, you'll lose. But a determined student can ALWAYS find a way to go. Most people go to football games, but we aren't very good, so people usually go for the sake of getting drunk on a Saturday afternoon.
Dating in college sucks. Some people get lucky and actually develop relationships, but most people I know just have hookups (I use the term loosely - it doesn't have to mean sex) and have people of the other sex that they are associated with but not necessarily in a closed relationship with. I don't blame Carolina for the lack of a real dating scene; to me this seems to be the trend at all colleges.
Freshman year, most people's closest friends are the people they live with or the people they hung out with at orientation. For some people, this continues on throughout college, but for most people, new friend groups are formed as they no longer live in the same suite. I had various friends freshman and sophomore year, from dorms, clubs, etc., but my best friends were formed when I joined a co-ed business fraternity on campus. These friendships lasted because I saw those people more often (they were in my classes, etc.), because we had similar interests, and because the social scene changes a lot when you are able to go to bars (either because you are 21 or have a decent ID).
As a junior or a senior, if I was awake at 2am on a Tuesday, there was a 100{4a082faed443b016e84c6ea63012b481c58f64867aa2dc62fff66e22ad7dff6c} chance it was because I was coming home from the bars. Tuesday is a fun night to go out, with lots of bars having great drink specials. The saying is that Tuesday is the new Thursday. Freshman and sophomore year though, I probably wouldn't have been awake at 2am on a Tuesday night, because I don't like to study late at night. If I had a big test on a Wednesday, I'd get up early that morning to study rather than stay up late the night before.
Some annual Carolina events include Homecoming (lots of alumni come back for the football game, and there's usually a concert for students that weekend), Late Night with Roy (begins at midnight on a day in October - it's the first time the basketball team can officially practice and Stuart Scott hosts the event), Halloween (it's HUGE on Franklin St - get your costume ready!), and this year SpringFest, which featured Boyz II Men.
Fraternities/sororities are far more important freshman and sophomore year than they are the next two years. Frat parties provide the main real party scene for freshmen, which gets old quickly, but once you are able to go to the bars, or your friends off campus start having house parties, you don't have to worry about that anymore.
What can you do on a Saturday night that doesn't involve drinking? Chapel Hill has a great local music scene, so there are always concerts to go to. There's also an independent movie theatre on Franklin St. which shows great films if you don't want to see the blockbusters out at Southpoint. I guess a lot of people who don't drink become friends with others who don't drink, so they create their own fun, but I don't know much about that.