Emily, sucks to hear you've not had the best week.
Personally, I've not experienced a bad flu like that for a few years but depression and loneliness can feel almost as bad, if not worse in a different way. Different pains... physical and mental I suppose.
Glad to hear you made a friend, ish! Hopefully you got her number/ facebook to chat/get more interaction going.
I don't have many friends at uni, but for the couple I do, I'd be very isolated if I didn't meet up with them all the time. Flatmates sound great, but the friends you really want are ones in your course so you have extra reason to attend lectures, and so a boring lecture is a little less boring!
Glad to hear you don't like proof by induction (one of the reasons I didn't want to do A2 further maths
) , but it's making a comeback!
Good to see you pulled yourself together to catch up. That's serious work and you did it!!!
I think I said it before, but the only way is up.
I don't know about friends from societies but what I do know is everyone's timetable is different and your degree sounds like it has a significant amount of teaching time, so yeah, friends from lectures/classes in priority!
About the whole partying thing... it depends on who you are I guess! I've not actually been to a party-party yet (awkward!), but it's clearly not the end of the world. I think the deal is finding happiness in the small things in life, and of course, one step at a time. To-do lists are great in that element, so nice work.