Cuthburt here, with your daily dose of Japanese Anthropology! First of all, I highly recommend everyone read Ruth Benedict's The Chrysanthemum and the Sword, OG publication was in 1946 but a lot of elements about Japan are still very relevant today.
So, to answer some questions. First: Why are all the psychopaths in the same class?
Japanese schools often lump all problem children into one class, and let the teacher they dislike the most deal with that class. This is due in large to the belief that, by sequestering problem children away from the remainder of the classes, children won't be corrupted. It also allows one teacher (who, as mentioned, is often times the most disliked teacher) to monitor all the problem children without the job needing to be split across classrooms. In general, no teacher believes they can fix problem/broken children.
Second: Not exactly mentioned, but the abrupt "yea I pushed you" moment, why admit?
Well, basically, Banri will never tell on this girl because of the nature of Japanese society. Telling on someone admits your own weakness and, in all honestly, will likely turn the teacher against you too (typically, I know within the confines of this Manga that is not the case). Teachers in Japan are notorious for joining in the bullying of their students, and blaming problems such as vandalism of a desk on the student in question. It makes a sick kind of sense that Banri will not tell her teacher "who did it." To make matters worse, as already seen, the school wants to cover the whole thing up (which is pretty normal for Japan) but Momo prevented that by talking about it online. This throws the school into a freak out mode that because they don't really want to find out who bushed Banri. Banri being pushed just shows that she needs to fit in better with her class.
Lastly: "How can the chairman throw something at Jimi and get away with it!?"
Sadly, things like this are not uncommon in Japan. So called "black companies" are know for their abusive dealings with employees, and with Japan's general belief in a lifetime employment system, changing jobs is all bot impossible after you have finished your third year of university. Though the direct physical abuse is likely played up for the purposes of the manga, getting a job teaching in a prestigious private high school would likely be considered worth any abuse thrown your direction. As a note that is not anthropologically related, it does seem that Jimi and the chairman somehow know each other, and that his general response provoked the act of violence from her.
If there are other questions I missed that anyone wants answered, tag me and i'll do my best to answer them (as long as they pertain to the manga). Otherwise PM's are fine too.
As an aside, none of this excuses the pacing or new character additions or whatever from a stylistic point of view. But I did notice that a larger number of people were confused at the social aspects of this manga because they are so alien to foreigners.
edits for formatting