All this newness, trying to get on with people you don't know, sorting everything out for yourself, coping with uncertainty, worrying about your course -- is the same for everyone. Some people are just better at covering it up. Just because they appear to be coping, doesn't mean they are. The way to cope is to be as nice as possible to everyone you meet, knowing they feel like you.
All these 'problems' are why you have to go away from home, to Uni. This is how you grow up ie take responsibility for yourself. I would not recommend you go home soon. You need to be with other people in your situation so you can sympathise with each other. This is how people bond. If you split away from everyone else you will be making making friends that much harder, setting yourself apart from everyone else.
Be as flexible as you can. Go out for a drink - heavens you can have a coke can't you? You don't want to gain a reputation for being difficult, stand offish. Don't wait for someone else to suggest what to do. Invite them in for a coffee , a cry over a good film, a game of snap, a look at your new coat, make suggestions about a new hair style...whatever...smile, smile, smile. Be self deprecating but complimentary to everyone else - you like their top, aren't they lucky being so tall, clever, pretty, etc. Small talk is very, very important - it's what makes people feel at home with you , feel as though you are interested in them.
You are used to being with family and friends who make allowances for you, humour you etc. You have to be able to get on with people who don't know you, don't have the same interests as you, learn to make new contacts- this is what being grown up is about. You are going to have to do this when you get a job, give a talk, meet new clients etc. in the real world.
Right so write down a list of 3 things you need to do today -
1)Knock on someone's door and ask them to join you for a coffee and chat, keep going until someone says yes.
2)Say something nice to 3 people - I like your jacket, shoes, hair...
3)Ask 3 people where they're from, have they left a bf/gf behind, why they chose their course, how many brothers/sisters they've got .....
You'll feel much better with a plan of how to survive.. and great when you've done someone a good turn.
Think , you could be a member of one of those tribes that send you off into the forest to survive on your own for a month. This is easy in comparison!