Personally I don't approve of "youth custody" and I believe that the age of criminal responsibility should be defined by the time when the "responsible adult" decides that the child is mature enough to, and therefore allowed to, make their own decisions.
Crimes should be judged and sentanced without taking the age of the offender into account - if children are allowed in a public place unnacompanied then the adults that allow them to be there are deeming them criminally responsible and they should be tried as adults whatever age they are. I think it's the only way to defeat hoodie culture.
As for capital punishment, that's more difficult... maybe a "death row" for a minimum of 10 or 20 years would be effective, to give time for all evidence to come out before execution.