It depends what you're trying to say.
First some notes about the statements without the negatives:
"Look in the box." is in fact more common because normally we're trying to say "Look for it in the box." (Cupboard, bag, etc.)
If you are giving precise interactive instructions/directions to someone you might use "into" - "Look into the box." is slightly more emphatic and contains a hint that the person shouldn't be looking anywhere else.
"Don't look in the box." can mean either don't search the box or don't look inside it, it might be a request or it might be a warning. Either way, whoever has said it would prefer you didn't see the contents of that box.
"Don't look into the box." is more emphatic and comes across strongly as a warning. It doesn't suggest that there are contents which should remain unseen, but that the act of looking inside it could cause you harm.
Unfortunately, no. The imperative in Italian is much more complicated than that. It's true that the informal second person singular (tu form) negative imperative is just "non" + the infinitive. But that is the only case in which the imperative and infinitive are the same.
Here is a link: Italian Imperative