The reason why Takashi is at Cromartie in the first place is explained in the manga and the movies, though he tells the audience to just read the manga instead of explaining it in the anime too. Toward the end of his middle-school years, Takashi became friends with a delinquent called Ichiro Yamamoto. Although Takashi was able to enroll at a much better school, he decided to prove to Ichiro that you can study in any enviroment, and they enrolled at Cromartie together. When it turned out that Ichiro had failed to enter the school, Takashi's new goal became to make the school a better place.
When three people from Takashi's class were supposed to be chosen as candidates for their strongest member (implying leadership), Shinjiro Hayashida nominated Takashi, comparing him to a rabbit who lives among a pack of lions and who should be seen as more badass than the lions. Takashi won the competition in the end, and may have used this to make his classmates act more civilised. For example, he teaches them how to have normal, boring conversations in an early chapter.
Takashi seems to have a knack for mechanics, considering how he once turned Shinichi Mechazawa into a fully functional motorcycle without even attempting to do so.
He is friends with Shinjiro, Akira Maeda and Shinichi. His pseudonym Honey Boy (which he uses when sending jokes to the radio station and on the internet) unknowingly has a rival in Noboru Yamaguchi, and Yutaka Takenouchi is aggressive toward Takashi out of paranoia stemming from their first meeting.
Neither Takashi's name or his female form's name (Takako) are references to anything, perhaps serving as a way to make him seem more like an ordinary person.