Why did Kevin do the school shooting, and why, in the end, does he suddenly regret it and does not know why he did so?

No one seems to know exactly why Kevin carried out such an appalling act of mass murder. If anything, that makes his actions all the more horrific. We know that Kevin's been psychologically damaged for quite some time, so there's a grim sense of inevitability about the high school shooting. Kevin appears to have all the hallmarks of a sociopath, and his behavior is perfectly consistent with this diagnosis.
There's no evidence to suggest that Kevin feels any remorse for his wicked crimes. In fact, he tells his mother when she first visits him in jail that he knew exactly what he was doing, and that he'd do the same thing over again if he had the chance. So I'm not entirely sure that Kevin really does regret what he's done. Perhaps it only appears that way because Kevin, towards the end of the story, is frightened at the imminent prospect of being transferred to an adult prison. It's the only time when he see him displaying any kind of recognizably human emotion, the only time he appears in any way vulnerable.
But if we accept that Kevin is a sociopath, then this kind of behavior can be seen as displaying self-pity rather than any in-depth emotions. As always, Kevin is only thinking of himself and his own needs. When he tells his mother that he doesn't know why he committed the murders, but that he once thought he did, we're not quite sure what to believe. However, there's a strong suspicion that he could be manipulating Eva, playing on her emotions to make her believe that there's some dark, terrible secret lurking in the tortured depths of her son's troubled brain, and which will provide her with the answer that she's been looking for all this time.