Spoilers for the novel side:black&white ahead.
Kuro had a happy family until he was 5, when his parents died in a car accident. He spent two weeks in the hospital for rehabilitation before he was taken in by some of his relatives. Those relatives died soon thereafter from a fire, and Kuro was treated as an unlucky child, and most relatives wouldn’t take him. He was eventually taken in by a distant relative, who was the worst sort of scum (alcoholic, gambler, shit deep in debt). Kuro was constantly abused and wasn’t even allowed to go to school. One day, even that relative went out and never came back. Kuro waited for a whole week before realizing that he’d been abandoned. Sick and weakened, he left his house and wandered in the snowy mountains before Ichigen found him, on the verge of death.
Ichigen found Kuro because he saw Kuro in one of his visions. But the only way to save Kuro at that point was to make him into a clansman. “I’ll put an end to all that misfortune that befalls you.”
Days of training follow. There’s no telling when a clansman’s ability will awaken, so training is the only thing they can do. (Oh….so this was what Red meant by Kuro’s powers awakening…so Kuro is not a Strain but a clansman, confirmed).
The school that Kuro attended only had 4 students. Their homeroom teacher was a woman who was quite infatuated with Ichigen ever since she visited Kuro’s home. Watanabe from the Kuro manga also appears in this, and offers to teach Kuro how to make dashimaki (Ichigen also learnt cookery from her). Kuro said that he’d like to learn everything he can from Ichigen before trying his hand at other things.
One day, a student from the school went missing, and Kuro himself went to search for the student because Ichigen happened to be away. He found the student, but both of them nearly fell off a cliff. This was when Kuro’s clansman powers awakened.
In the end, he takes up Watanabe’s offer and asks her to teach him how to make dashimaki.