Most universities will guarantee accommodation for firmers, and insurers will almost certainly get a place or private halls will be available so maybe it's slightly overstressing?
For the social side you'll be ok, there will probably be a few other people from your university there if it is not the majority and usually you would be put in a flat together. Yes you can go to fresher's events at both universities. Freshers events, outside the stuff you do for your course, are more about making friends with your flatmates than people at the university so it won't make any difference. (In general you don't make long term friends during fresher's unless they're flatmates or coursemates, so again don't worry).