Snoozing or Unlisting removes the listing from the search system, so you only will not recieve booking requests or inquiries. Deactivating will remove the listing (and so the belonging calender) !
Inbox will remain, it is not related to listings, but to persons.
Everything in your hosting account remains accessible to you when you snooze- snoozing just means the listing isn't visible to guests. I'm not sure how deactivating works.