Short answers, pulled from the story.
Kazue Kato debuted in 2000 with a one-shot published in Akamaru Jump. She went on to publish several more one-shots before launching her first full serialized series, Robo to Usakichi, in Monthly Shonen Sirius in 2005.
Blue Exorcist began serialization in Jump Square on the 4th of April, 2009. It was developed after the editorial department of Jump Square approached Kato directly following the completion of her first series.
Blue Exorcist was the first manga in Jump Square to achieve an initial print run of one million copies for a single volume, a milestone reached with the seventh volume of the series.
Kato has cited the shojo manga magazine Ribon, Gosho Aoyama's Yaiba, and the works of Katsuhiro Otomo as early influences. She has also identified Kentaro Miura's Berserk as a major influence, particularly the relationship between Guts, Griffith, and Casca.
In July 2021, Kato announced a hiatus for Blue Exorcist so she could create a manga adaptation of Fuyumi Ono's Eizen Karukaya Kaiitan novel series. That adaptation was serialized in Jump Square from 2021 to 2022.
In 2020, Kazue Kato provided character designs for the Godzilla Singular Point television series. It was a departure from her serialized manga work and drew on design skills she had expressed interest in since high school, when she originally aspired to become an animator.