Come species of ammonites had a plate called an "Aptychus" which some scientists believed the ammonites used to cover the opening in their shell. However other scientists believe this structure was used more like a jaw, or as a support structure for the ammonites mandibles.

I do not believe that ammonites have/had a cover. gastropods did and do. completely different creatures. the term for the cover is operculum.

No the exit of its shell was open. It could hide inside its shell but it couldn't close it.

In one of the Walking With… documentaries (I think it was Dinosaurs), some ammonites are seen retreating inside their shells and then closing it with a sort of lid. Did this lid actually exist? Do nautiloids have a similar structure? Where would the lid be when open, if it did/does exist?