A lot of what you say, I recognize. I am 33 years old. I have been in 7 different schools/colleges. I should be an expert at this by now. I suspect that years of mental illness/self-isolation and reducing social interactions only with my toxic parents, that ruined my personality, maybe permanently.

I think about this subject every day, but make baby steps only.

For others, it is second nature and seems to go automatic. Yes these people may not even have beeen truly in love before, may not have had any setbacks in their lives ever, yet they know more than I do.

It is not impossible to be in two groups. I did that once, when it still went automatic for me.

Anyway, 'friend groups' isn't what true friendship is. They happen indepentent from that. Like JustMeMyself&I says, they are friendships of convinience. People like some people in the group, dislike others. And that is ok. True friends you only become one on one anyway.

Who do people decide to hang out with during breaks? Why do some people start to hang out with each other after class hours, and others do not? Why do some people become friends and not others? It is largely a mystery to me.

After my mental illness, I went back to school. At the first school, I didn't even try to interact with others. I never talked with anyone outside class, ever. I barely knew anyone's name. I was 29, everyone else was 16-21 or so. I was pissed to be there, because I didn't learn anything. I knew everything already. I just didn't have the correct piece of paper to move on. I only remember one guy ever really trying to talk to me. But I guess I shut that down. And I remember one girl being really impressed with what I knew while having a group assignment. I knew two of my teachers were younger than me. And the third may have been as well. Even at the exam ceremony, I went to say goodbye to one of the teachers, trying not to autistic, and he just asked me: "I never understood why you were even here, what you role was?"

At the next school, I kind of had some ideas about trying to do better. We had a group of 14 or so students, doing all practicals together. They would all sit together during breaks. One group, not two or three. The mentor teacher later commented on that, saying it was unique. It wasn't because of me. I felt really awkward. I knew that they felt uncomfortable if I distances myself from them. But sitting with them, I just learned I had very little in common with them and very little social skills left to banter.
I was just there to fight hard to make sure I had some kind of professional life, and to destroy my past education demons. They were just there because it was the next step in their life. Most of them would say: "My favorite part of school is the lunch break." I disliked the lunch break. It just meant I would have to stay at school and be away from home for a longer period of time.

I vividly remember one case where we had a 2 hour gap in our schedule and me and a nice social girl were supposed to work on a group project. I sat down with her and some of our classmates, expecting her at some point to say "Ok now me and him are going to work on our project?" She never did and I just sat there for like 1.5 hours, listening and barely saying anything.

One guy eventually did something to engage me in the discussion. I think they were talking about children, so he asked me, knowing my age "So do you have any children." Not sure if that was a joke or not.

I also learned people don't ask for your help just because you know you ace all tests. They have to really like you before they ask. Or really like you and think you are great at explaining things, and ace all tests.
They will also not form a group with you for group work, knowing you work hard and produce good results. They just pick their friends. And I always just let that happen. So it was always me and whoever else was left, ie the most lazy, most awkward or most passive students.

I guess what was most puzzling to them was how I would take charge and be dominant during discussion sessions that were part of the curriculum. But that was talking about science, not talking about things that 17-22 year old talk about.

We had to give each other anonymous feedback. I always got "He knows a lot. He works hard." as the positives and "You are arrogant.", "Don't try to place yourself outside of the group" or "You are insecure." as the negatives.

Vocational college was too easy, so I tansferred to university. I had all these cool ideas about how I would learn from my mistakes and do better. I hoped to make new friends somehow. And I couldn't see how that could happen giving how I interacted at the vocational school. So I had to do something different.

I think I am doing a bit better. I can control things I say that make me sound arrogant. I am less insecure and awkward. The 20-something small talk and banter, I can fake it a bit now I guess. I can even say things sitting on the top of my mind now, without restraint. And act a bit more animated/dynamic.
Still, I don't say a lot when we sit in a group during lunch and I always recall people saying that when you speak rarely, people will listen when you do. I always had people talk over me and ignore what I was saying, ever since childhood. I don't see it happen to others. Twice so far a 20-something girl with strong social skills had to intervene on my behaf and tell everyone else to be silent because I wanted to say something.
I managed to have good working relationships with almost everyone and I now know everyone's name and something about who they are as a person. They will say 'hi' to me when we meet in the supermarker.

But I have not made any friends. I don't know who out of all the people I met I actually like enough (except one girl but that's a different story, long long story). I also haven't seen any signs of someone very eager to be my friend, and I guess that is what I want and need for me to do my side of the investment/risk/whatever you call it.

I would say that making friends in college is very easy. Maybe making true friends is a lot harder. But something is wrong with me as a person. For a normal person, it is not so hard. That includes insecure people. Everyone has the same problem of suddenly being in a new town and not knowing anyone. But there are tons of people that are almost just like you, if you are a traditional student.

I feel I am supposed to give you the master equation now. But there is none. You just have to be an open person, willing to take risks, willing to be rejected, shameless about shallow thoughts others may have of you, not overthinking everything. Basically the exact opposite of what I do.

You just form little shallow relationships with people based on just one shallow silly similarity you have, besides both being a student.

And then somehow you have to become a cool fun person so people think "this party/activity would have been so much more fun with X". But I guess that stage is not for most.

That said, I don't understand how it is actually done. I went to fencing today. There were a bunch of new people. I hadn't been there for 2 months. During breaks, no one actually said anything to me. And I didn't say anything to anyone else. I don't know if anyone noticed. I like to listen to two other people talk, then jump in. That's my trick. And when I notice some other person is even less socially skilled than me, I don't even think about talking to them. I wonder if people feel I am unapproachable more than they think I am not fun or boring or awkward.

Back to your situation, I guess my situation is a bit different. People try to talk to me, and I either shut them down or make it so boring, they start talking to someone else.
You are not bullied anymore, right? Being bullied because you are bad at English, well at least that is better than being bullied for who you are as a person.

I also recognize your studious vs backbenchers case. But groups didn't always split down that way that strongly. I also felt that sometimes there would be a group where the people who don't belong anywhere else are. And then the 'cool people' would leave if there are too many of those. But the whole 'I cannot talk to you with lunch because your grades are poorer than mine'-thing, no one responds happily to that. Best thing you can do is never show any disrespect for even the most lazy or stupid fellow student.

Basically what I did during lunch was just look around for people I knew, and sit down with them. I was never refused. I suspect my fellow students use Whatsapp to meet up during lunch breaks, or that they have other groups of students, like year clubs, fraternities or dorm mates, that they hang out with during lunch.

As for a psychologist, I don't know if it will be hard or easy to talk to one, but surely your parents opinion don't have to come in. They won't know about it. Or do they have to know because of money issues?