Hi friend
First off, I am feeling the exact same as you are. I was so excited to get away from high school, which in the end made me severely depressed and much more, but so far university has not been too good.
About not being able to go out/make friends: is it really worth it if they aren't even real friends and don't bother to keep in touch? Meeting people at socials/ when they are drunk usually don't make good relationships anyway I have found. I too have always felt that nobody actually wants to befriend me, and instead of saying to you 'force yourself to make friends' etc., I say just stick to yourself for the moment, if a true friend will come along then so be it. If I were you I'd try sitting next to people sitting alone in lectures, they may be in your situation. But it is really important not to isolate yourself, so do keep in contact with family- try and phone daily if possible, it will help trust me.
As for the workload: make this your main priority, if you feel more depressed in your accommodation go to the library for hours to get the work completed. I'm not trying to say this to be a parental figure, but for me at least it has given me a motive to stick around at uni and, although taking a few weeks and still being quite behind, I have found that the stress and depression has diminished quite a bit. You still have time to get back on track with the work, so please do not worry about it and also don't overwork yourself too much either.
Finally, on a friendly note, I am in your situation and understand how hard it is. It's impossible to force the depression away, but if you just listen to my advice I hope it will help. Are you going to Edinburgh Uni by any chance? And another thing that has helped me for most of my life, and I am in no way forcing this on you but I promise it has helped me: tell God your problems, ever since I began praying again (I drifted away from it and the depression followed), I have felt free and truly happy. I am not saying this as a religious fanatic but as a friend that cares, and believe me God does too, even if you do not believe in him at the moment.
Please don't give up just because of meaningless things, the depression will wear you down unless you fight it! And finally don't be hard on yourself please, you seem to be a really incredible person from your post, and you are real and a true friend, unlike the majority of those you will encounter getting drunk every night/with crowds of friends. Trust me they are not happy either, it is just a front.
Any time you want to chat please just say, and all the best to a happy future