Can this be "is he hurt?" or "is he injured?"
Does it refer only to sickness or can it refer to an injury?
It could fly as a statement when you don't want to be precise about what has happened to him.
But I think that as a question your examples would work better as "Он ранен?" (in case of violence) or "Он травмирован?" (in case of something self-inflicted and more)
Edit I mean that "Он болен" could cover your both examples if you want to be evasive
Thanks. In that case, I think "Is he hurt?" should be allowed. This is the usual way in English of asking if someone is out of action, without specifying what has caused the damage.
You are right, probably not. It does imply some harm, even if mild and temporary, as opposed to simply subjectively not feeling very well.
What did you mean by "something self-inflicted and more" in your explanation of травмирован?
I should add that "травмировать" does not exclude intention. "Он специально травмировал нашего лучшего игрока / Он специально нанёс травму нашему лучшего игроку" is absolutely possible in sport too. But "ранил/нанёс ранение" sounds even worse to me. And even this can be an accident. One doesn't know that a gun is loaded and accidentally shoots someone in his leg for example.
It's a bit difficult to define in one comment.
I meant something that was not intended by anyone the way it can be in case of violence (it is not a very precise definition of course). An accident.
I wonder whether my definition of "болен" comes from "быть на больничном". It's when one is officially not fit for work for some time.
@Zeitschleifer: interesting - when you mentioned violence I did not assume that it was deliberately inflicted. Falling off a cliff is a violent accident even if you simply tripped and fell. It indicates sudden and traumatic injury - the body getting smashed, bashed, and broken - rather than presence or absence of hostile intent.
I would not recognize falling off a cliff as a violent accident in English. Something to learn again...
Violence = насилие in Russian. Насилие, насильственные действия in Russian require an object and a subject in my opinion. I don't see it in case of someone unintentionally slipping off a cliff on his own