Hi
I've just started at uni as a mature student, so I can understand where you're coming from. I don't think I look my age (39), but then that could partly be my own vanity talking! I have no idea how old others at uni think I am (haven't asked them), but even in my wildest dreams I can't imagine they really think I'm in their age group. It's also likely it's pretty obvious I'm an older student since I tend to speak up in seminars more than most (though not all) of the younger students are doing at this early stage.
I'm also living off-campus - I've moved to my uni's town more or less on a full-time basis. I might go back to visit my family during holidays, but in essence this is my new home now. So I'm in a new place where I don't already have a pre-existing network of family and friends.
Not living in halls is almost certainly the right thing for most of us on the more mature side - a couple of mature students on my course I've met are living in halls, but then they're only in their early 20s, so the age gap isn't that great. I'd imagine for most people over 25, living in potentially messy and noisy halls is about as appealing as having teeth pulled. Downside is that I'm a bit out of the loop. It's taking me longer to get accustomed to finding my way around the campus, since I visit there rather than live there. Plus there's the overhead of getting to and from campus from home to contend with, although in my case it's not too bad as I live about 15 mins walk away. But still it's a pain, and events and amenities at uni aren't literally up the road from me as they would be if I were living on campus.
I don't have the long range view of it yet, since it's only the end of Week 1 for me. However, my feeling is at this stage that it just takes a bit longer for some of us to get integrated. I'm also in a situation where I need to, simply put, get my life together a bit while I settle into a new place. This is in a quite physical sense - I've got boxes of stuff that I've ported over from my old abode that are all over my room, and I need time to sort them out. So I'm not jumping at every possible social opportunity at the moment - my weekends so far have been pretty quiet.
I understand your worries. I turn up to things (lectures, seminars & screenings) and it's a bit disconcerting since people already seem to know each other. It's the same thing at the clubs - despite this being touted as the standard "cure" for having no friends, people already seem to be friends with others right from the first gatherings of these clubs, so naturally they go there together, sit together, and chat together. It's a bit hard when you're always going alone. If you're not a particularly forward person, you don't want to constantly be forcing yourself on people. It's much worse when you're constantly thinking, "are they just not going to accept me because they don't feel comfortable with an older person?"
So, you're not alone in being alone! I don't have the magic solution (yet), unfortunately. My strategy is just to keep quietly plugging away, and hopefully in time the younger ones will grow to disregard the age factor. The other thing is find out what's going on with your uni's mature students' society. If there isn't one, maybe set one up! We had a Week 0 mature students session for my subject - only 4 turned up, but that was a great ice breaker. So anything mature students related is worth going to - I've also signed up for a networking lunch in November. One piece of advice I got at the earlier session I mentioned was to embrace your mature student status but not be an isolationist.
Sorry, this is a really long post, but I've noticed that when people post these questions (as I have in the past), people tend to respond with well-meaning but not all that useful platitudes ("Don't worry, you'll be fine! Just be friendly!" etc.) It would be interesting to hear from people who have got involved in the standard societies (other than the mature-student-specific ones) and how they've handled it. I find myself asking, "if I go on the <such-and-such society> social/pub crawl, will it be a key step in overcoming the barrier, or will I just be the sad old git in the corner no one wants to talk to (except out of pity)?"