It's not as traditional in terms of like gowned formals etc., but that doesn't mean they don't have plenty of college traditions, which I'm fairly sure pretty much every college will have
It does depend on the formal, but in general friends can invite you to gowned formals at other colleges (but expect to pay a bit more for them since you won't be a member of their JCR). Some colleges do prioritise their own college members, or for specific formals say only their members can attend though, so it requires a bit more planning!
The first question depends massively if you're in college or not. If you're in a catered college for instance then you had all your meals delivered, and many colleges were allowing one household out at a time for some exercise (since you were meant to be isolating from each other too so were basically confined to your room). If you were living out then I don't think any support was automatic, but it was available if you needed it iyswim? Welfare support is always available for all students at any time, practical support was more a if you ask then they'll sort it type thing. Most livers out would have got friends who lived nearby to for instance drop off food if they couldn't get a delivery etc. rather than asking their college, but I'm sure the college would have arranged something if necessary. There's also a specific covid hardship fund if you were financially hit by covid (eg. by parents losing job etc.)
Online teaching varies per department (or even by lecturer tbh). For my department the provision has generally been very good, we get pre-recorded lectures for almost every module which are actually better than live lectures as you can pause it, get something repeated etc. without having to get behind while trying to figure it out. You seem to come out with a much better understanding at the end of it which is a massive benefit! We also have an online forum for each module for questions which the lecturers answer regularly, and live Q&A sessions with the lecturer 1-2 times a week. In-year assessment is the same (and indeed is for many subjects), just with online submission (which many subjects did pre-covid and I'm hoping my department will stick with post-covid). Exams aren't ideal is probably the biggest problem, we're getting 24 hours with open book, but because obviously that's much easier than 3 hour closed book exams then they're having to make them a lot more difficult or they become impossible to standardise, so not looking forward to that!
I'm not a first year, so I may be unaware of activities that were put on specifically for first years but it's not really specifically Durham's job to put on those activities, it's down to the colleges and SU. So in my college (and I'm sure the others), I think there's 5 times a week welfare chats which are run by the welfare committee but are an opportunity to chat to anyone there. Societies are running as much as they can, but online obviously. Some of the big societies such as Durham Student Theatre are running a lot of workshops and doing online shows etc. Colleges have opened up a lot of spaces for you to use within your household, for instance my college allowed households living in college to book the gym, the JCR lounge and spaces in the bar such as the pool tables. When it was allowed the bar was open and you could sit with your household etc. Most things in person had to be in households because Durham was tier 3/in lockdown for most of term 1, so that meant no indoor mixing between households legally and obviously they can't go against that! Online there was plenty of opportunities to mix though.
Households varied by college, definitely not as big as your college, because that would probably have meant the whole college was in isolation most the term! In catered colleges I think a corridor was typical, which tends to be around 20, although I have heard of households up to 37. Even in colleges where you were in flats, then they tended to put 3 or so flats together to form a household of around 20 also that you didn't need to social distance with.
In lockdown 1 when we were all sent home (and the vast majority of people did go), almost nothing was open, I think the library was postal service or click and collect only, and I imagine the sports centre was completely closed as was required by law. In lockdown 2, very little actually changed from the rest of term, the library was still open 22 hours a day (2 hours closed for cleaning), booking only, along with other places to study and teaching continued in person where it had been for the most part. Because schools stayed open, they were able to do this. The sports centre did have to reduce itself to household groups only, and you had to book for a household session if you wanted to use it, plus in my college you could borrow equipment from a college team for a while to use in your household. In this lockdown, obviously most of us haven't gone back to Durham because of the lockdown beginning before term started. The library has cut it's opening hours to I think 8am-10pm, still booking only, and reopened it's postal service for all the students not in Durham (though I think it's limited in some way possibly? My course doesn't use books really so I haven't been paying the most attention to it, but I think it's possibly for students doing research projects only rather than just essays). The sports centre I think is closed this time, but the other study areas are open for booking. Other services I think have been online throughout, for instance all the councilling services, careers service etc.
I'd say Durham has done a pretty good job in terms of dealing with it. We've been getting at least weekly emails since last February about it (daily at the point we were being sent home/they were sorting everything), they've refunded the rent for students living in college both times we've been in big lockdowns, and indeed when it was suggested students should have staggered returns they were going to refund the 2 weeks some courses were delayed by to those students. There's an absolute tonne of support of all types if you reach out for it from colleges, from the university, from societies etc. They're proactive about keeping us updated and if they don't have an update (eg. when the government announces something about unis but they have to work through it), they usually tell us they will send an update by x day so we know. Every time the rules changed they worked to get as much open they could during that time, often everything would be closed for a day or two, then they would assess what was allowed and reopen anything they could.
I will add a lot of this is my college, so it's possible other collegs aren't so proactive, but I would expect at least most of them to have been!