Is There a Subpage Builder in Kirby 3?

Do we have a Subpage Builder in Kirby 3? - or do we have to use hooks?

You have to use hooks, but see the upgrade guide for a blueprint-based replacement: => Remove blueprint-based subpage builder

Thank you, @texnixe! Follow up question: how does deletion in this case work? Do we also have to implement a hook to automatically delete the children pages when the parent page is going to be deleted?

No, just like in K2, if you try to delete a page with subpages, a modal pops up and asks to confirm the deletion