I believe просить means "ask for"/"request" whereas спрашивать is simply "ask".

That sounds rather like he's asking about something called "In the box", or what being in the box is like.

I think I see the source of your confusion, because if someone asks "Where is the box?" you would say "He asks where the box is." Even as a native speaker, I'm not sure I could give you the general rule, but I can explain this specific case.

The question "What is in the box?" is already in standard word order. You could answer "The cat is in the box." But "Where is the box?" has a transposition, because the answer would be "The box is there." Occasionally you will even hear English speakers ask "The box is where?" -- it's a bit of a clumsy word order but still gets the point across.

So in the sentence "He asks where the box is", the original transposition is removed, and replaced with a different one, because we like to put the question word ("what", "where", etc.) right after the verb "asks". We're not moving the verb "is" to the end, we're moving the word "where" to the beginning.

I am not a native English speaker but I think Yuri is right. Can a native English speaker help us?

This sentence isn't a question but a statement. But "what's in the box" is the question. Then where is the sign "?" at the end?