Just some comments about your post. First I want to give you a link that might help your overall writing:
menwithpens.ca/how-to-add-flow-to-writing/In the interest of not seeming extraordinarily lazy (which I can be, so don't get any ideas that I'm not), I'll explain my take on it. Personally I think flow is one of the most important qualities you can have in writing. With flow, you can make the simple and mundane easy and accessible. Even with very complicated ideas and wording...with proper flow, it can make these things both manageable and beautiful. Just to give one very good example...Twilight.
I personally hate this book for more reasons then one, but the most relevant reason for this review is that it is very poorly written. Yet it's earned world-wide fame. How? The sparkly vampires help I'm sure, but the book has such good flow that, despite it's simplicity and the fact that it's just...bad, it's easy to read and people aren't apt to put it down. With flow, theoretically, you can be a terrible writer and still captivate millions.
(I posted this in Ageha's app:
clannadrp.proboards.com/thread/2538/verdiano-fujihara-regina-ageha if you want to check out the original context. It may help you understand my point more clearly. Sorry in advance Atena)
With all of that said, I want to say I do like your role-playing and I think the content is very good, just that it may lack flow and overall cohesion from paragraph to paragraph.
So let's move on to the RP sample and if it fits Kotomi. I have two main things I want to address, first being Kotomi and her parents, and second being the character of Gray, who I believe is an OC created for the purpose of this RP sample? If I'm wrong you can correct me.
"Kotomi found all of this highly fascinating". Are you sure this is the case? If we remember from the show, Kotomi originally dived into the same thing her parents were studying due to feeling responsible for there deaths. In fact, rather then diving into the same field of study...often times she would just cut out any mention of there name and keep that on record. Presumably this did lead to some development and understanding of what they were trying to study, but it's unlikely this was her primary goal. It's more likely she reads up on as much knowledge as possible in the hopes of finding any mention of her parents so she can keep a copy of it with her. This is also probably why she has a wide girth of knowledge, rather then just being highly knowledgeable in one field. It's possible she may have an interest in the same field of study as her parents, but when we first meet her this is unclear. In fact, it's not even clear if she understood what her parents were studying. We learn, not from Kotomi, but from her Godfather what there original objective was. It's not until the completion of her arc that she seems to understand and truly find peace.
Then there's the next paragraph "A single tear rolled down Kotomi’s...trying her best to cope." You mention how she's managed to push it away but it's not indicative of her being over it...but are you sure this is the case? It's actually very possible that Kotomi may have pushed it so far away that she's barely aware of it anymore. Think about it. A shy, quiet girl with no real friends or family to rely on. She lives alone and the most company she usually receives are the books around her. Even on the off chance someone comes in to check on her, she usually doesn't even notice there presence as she's so absorbed in whatever she's reading. There's actually a very high chance she has pushed away the memories of her parents and her past completely and is losing herself in the books around her. Gaining more and more and more knowledge without entirely knowing why. However occasionally, she'll see a mention of her parents, and in some type of stupor that she herself doesn't understand, will begin cutting it out. This behavior is actually contradictory to her nature, as Sunohara once made a huge ruckus beside her and she scolded his behavior of treating the books poorly. She respects books just as much as anybody else, but her need to cut out and keep mentions of her parents are ingrained in her. In fact, this is probably the last tie she has to her dark, dark past. This habit she has formed. Other then that though, it's very likely she's lost in her own world - her own space, and it isn't until Tomoya stumbles upon her that anything changes...which can likely only happen because he was a part of her past that she banished. There's even more evidence for this in her arc. When Ryou gets into an accident how does she react? That's right. She breaks. This would not happen if she had been carrying this with her this entire time. It would really only happen if she had pushed it away entirely and had lived in her own world for a long time. Everything comes crashing back and she locks herself up in her room.
So now on to the latter half of the RP with the introduction of Gray. I can understand why this character may exist in the context of this RP. It's important to show how a character interacts with others, so it makes sense to introduce a new character for this purpose (again, if this is a pre-existing character with a developed relationship with Kotomi just let me know), but I have several issues with this in context with there interactions as well. I'll try to keep complaints about Gray brief as he's not the one being reviewed here. You do explain that he's practically a stranger and he visits for class updates so I'll continue with the basis that that is everything to know
Why does he call her Kotomi-chan? If they aren't friends, she would have never been able to give her classic Kotomi introduction. Usually she *tells* the other person to call her that, as it is a very childish type name. To begin with it's surprising he calls her by her first name "Kotomi" but with the addition of "-chan" it's even more surprising. The rest of his dialogue also seems a bit unnecessary. Also the way he casually throws her a handkerchief is a bit odd and seems almost cold. Does he always catch her crying so he knew to have it handy? No words of encouragement or asking if she was alright? If they were friends or comfortable around each other that would make sense, but as strangers you'd expect some more courtesy.
I don't mean to harp so much on this one-off character, but it's important for characters who interact with Kotomi to be also be fully developed, or at least realistic, so that you can have an easier time role-playing. If I was role-playing my character and all of a sudden some naked girl burst in the room and fell on my character with her crotch just happening to land on my characters face, I would have no way to reasonably respond to it. I would either just have to not post, or post SOMETHING in an attempt to continue the RP but likely compromise my character in the process.
So this also colors the final paragraph. While I can question Kotomi's behavior as an individual, it's difficult to question whether she acted appropriately in regards to this specific character as he himself is an enigma. Kotomi seems really calm and collected here. I can see you're going for her quietness and deliberate way of moving and speaking, but there's a delicate balance that comes into play with Kotomi. It's very possible for her to unintentionally be rude or make a mistake, but she does so in such a way that a child would - innocent, and harmless, so people are quick to forgive her. Here I'm not sure if she would talk to him without at least looking him in the eyes. Again, it seems almost cold.
Finally, I'd like to say a little bit that's not specific to any part of your post but is, again, a more broad statement. Kotomi is very, very different from your usual character. She's kind of lost in her own world, and while she's capable of interacting with others, she is very odd in doing so. She tends to pull them into her world as others can't really pull her into theirs. This is why she can't seem to grasp very simple social cues or even have a conversation follow a normal pace. She's incredibly smart but also incredibly clueless, but she's so sweet and honest that nobody seems to mind her antics. Even if there ear drums have to suffer as a casualty. When reading your post I should get a sense of this. Just from the thoughts or the words or the actions it should feel very Kotomi. I fully recommend you listen to her
music (Notice how it's pleasant but also strange. It's kind of warped and follows an interesting pace but it's also very clearly kind and sweet) , as well as watch a few scenes of her interacting with Tomoya or the Drama Club (subbed of course) to understand this better. Really try and understand Kotomi and get inside of her head and then start writing and you may have an easier time with it.