As I understand it, a zombie process has died but still exists as a placeholder in the process table until its parent (or init if the zombie is itself an orphan) checks its exit status.
Correto.
And my understanding of orphan processes is they are processes that are still alive and running but whose parent has died.
Correto.
Since a zombie is already dead, its children would be considered orphans, wouldn't they?
Sim. Quando o pai morre, está morto. Com relação a seus filhos, não importa se os pais permanecem como zumbis: os filhos tornam-se órfãos no momento em que os pais morrem, e então perdem qualquer ligação com seus pais.
Would they be affected be reaping the zombie? Specifically, would init adopt them as its children only once the zombie was reaped, or would they be adopted as soon as the parent became a zombie?
Não, e o segundo, conforme acima.