We have the start of a compelling story here.
You have an ability to bring the voices of the several characters to life. Each has his own way of speaking, complete with energy level and degree of formality. This helps to distinguish the characters from one another.
You also have a good sense of getting the reader into the head of a character through more than just "let me italicize a thought". Things jumble without becoming confusing, giving us a good sense of how a person's inner being is acting, feeling, thinking. It feels fairly realistic.
The one criticism I want to discuss is the setting. I am familiar with the original source material that this fanfic is based off of. As a result, when you start discussing the various setting and personalities I know what you are referring to. However, anyone not already already familiar with it will be floundering about to understand the setting, how things relate to one another, and etc. Now, if the Kuroshitsuji fandom is all you are targeting, this is fine. It is not meant for an outside audience and need not be approachable and clear to them. However, if you are seeking a wider audience I'd recommend you flesh out the details to the degree needed to clarify for those not familiar, but not to such depth those already familiar with the setting will be put off by 'repeating the obvious' to excess.
You have a good framework going that clearly demonstrates your skills with bringing characters to life, and I encourage you to keep on honing that skill.