I'm not sure that I entirely agree with you that statements can't be made into questions in English. It's common when seeking confirmation of actions and procedures, viz.:
You entered the room? Then you turned to the table? You put down the book? You're sure you put it on the table? etc, etc
In French, when you invert the normal order of words in a sentence to form a question, you connect the switched words by a hyphen. ex: Normal word order would be a subject followed by a verb: Vous parlez anglais. (You speak English.) This normal order becomes flipped, or inverted, in a question: Parlez-vous anglais? (Do you speak English?) The flipped words are connected by a hyphen. The hyphen serves as a marker: it's a flag of sorts, to indicate that you have flipped the order of those words. This is not the only way to form a question, but it seems a pervasive and popular method. (This inversion also happens outside of questions, too.)
"Poser" is a complete movement from the moment the thing is in your hands to the moment the thing is lying/sitting/standing on a given place.
- "Posez votre arme !" is what cops order villains.
"Mettre" needs something else like a destination for the movement to be complete: "mettre sur", "mettre dans", "mettre devant/derrière" or even figuratively "mettre à disposition", "mettre en place", "mettre au point", "mettre en jeu"...
- The cops can say: "Mettez votre arme sur la table !"
Exception: when "mettre" is about clothing that you put on: "je mets mon manteau noir, aujourd'hui".