I started rewatching all the X-Men movies. And I'm surprised no one has written something like this yet. English is not my native language. So please forgive any mistakes. You can consider these as platonic or romance headcanons. Also, if you like it, please let me know.
I have headcanons that the Reader is telepathic like Charles, but also an empath and can influence the weather, but not as much as Storm.
When the Reader sees clouds gathering over the mansion, he/she can go outside and call out to nature: "Please rain don't go." And it will just be cloudy all day or the sun will come out soon.
I imagine that the first few times, until she accidentally saw it herself, Storm would think that someone at school was hiding their ability to control the weather, or didn't know how to control it at all, or she should go take a break.
The Reader's telepathy + empathy has a stronger effect on mutants. Especially on those who have animal features or turn into animals, have anthropomorphic/zoomorphic features. They feel quite comfortable around the Reader and tend to guard her/him for protection.
This means that theoretically the Reader would have had time to meet Wolverine's brother - Sabretooth, and they would have had a temporary truce in relation to her/him.
I feel that if Professor Xavier had allowed him to stay at the school, Victor would have taught the children how to navigate the forest, hunt, and make animal traps.
And most likely the children would have returned from his lessons cheerful and mischievously set traps for their friends in the hall and the room.
Until Wolverine fell into one of the traps. Now it was forbidden to set traps inside the mansion itself. But only inside. The children still practiced outside, which Victor was incredibly happy about.
I also believe that the Reader is no longer a teenager and is just beginning to enter the adult world. Most likely he/she is 21-25 years old.
And since she/he does not have to pay for rent or food, the question of clothes remains. And I suppose that the Reader, along with other mutants who don't have much pocket money, go to the city every weekend to find good things in second-hand stores. After all, some people give there completely unworn things! And other people leave branded things there. So I suppose that the teachers realized that perhaps the Reader should be helped. Because despite the small wardrobe consisting of good things, it is clear that they are already pretty worn.
Therefore, Professor Xavier offers the Reader to teach Physics/Drawing, to which the Reader immediately agrees, since he/she was a real nerd at school and he/she likes to study and also help others.
However, I also see that the Reader will have several new things in his wardrobe after this incident, for example: Scott's jeans, Logan's new leather jacket that Ororo gave him, Professor Xavier's black jacket, one or two of Jean's sweaters, Hank's checkered shirt… Perhaps the Reader and her/his friends share things with each other, so sometimes we can see Beast's shirt on Rogue's shoulders or Logan's jacket on Quicksilver.
Logan most likely, when he saw him in the jacket that he gave to the Reader, did not check with his own eyes. And the second time he took it away and returned it to the Reader with the words: "Don't do that again"
I also see that when the Reader wants silence or to be alone with himself, he goes to Hank's lab.
There they talk, drink tea or do their own work. Sometimes the Reader asks about how certain devices work or mechanism and Hank patiently explains. He likes this kind of company and is glad that it is mutual.
You are one of their favorite students, but they are unlikely to ever say so. Although sometimes it seems to you that you are indeed slightly distinguished from all the other students.