I have received many "friends" who have accepted my request when I don't know them, let alone requested their friendship! What are the possible explanations for this? Am I getting hacked? This has happened numerous times.
You can see pending friend requests now through Facebook without any extensions or add-ons. Click on the friend request icon next to your messages and notification icons and then click the link at the bottom that says "see all". When that pages loads you should see a link that says "View Sent Requests" and you can view them all there.
As others have said, it would be a good decision to change your password. I would also add that you should go into your apps (settings gear> account settings> apps [left sidebar]) and see if there's anything suspicious or that you don't remember and if so click "edit" then "remove app."
The only possible explanation of this is that someone had/has access to your account and sent those friend requests to random people who are completely unknown to you. Yes, surely you are/were hacked.
You should also install this Google Crome extension, with which you can see the list of people you have sent friend request and not received any reply yet: https://www.unfriendfinder.com/news