A couple of days ago, all of my mail disappeared from my Gmail inbox. I do not know if I accidentally removed it (I don't think so) or if some problem occurred at Google. Is there a way to search for mail which was archived during a certain time period? I just would like to know which emails were in the mailbox just before the emails were archived.
Unfortunately, no, there's no way to search by messages when they were Archived. ("Archive" just means "remove the special 'Inbox' label.)
The best you'll be able to do is to search by date range for when the messages were dated.
More importantly, though, you should check that there's not something nefarious going on. Gmail doesn't just do that "because". It's possible you've created a filter which acts on more messages than you anticipated. If that's not the case, make sure it's not some other third-party app "helping" you. Check your Google Account to see what app you have connected to it. Check also that someone hasn't created a filter you don't recognize. Check the recent activity to see if someone logged in from an unfamiliar location. (It would be a good idea to take the security check-up at "My Account".)
One other possibility: If you visited or tried out Inbox by Gmail and snoozed all of your messages, they'll be temporarily removed from the Inbox label in Gmail.