Question: New users cannot log in via Facebook, receiving an error message saying: "Application not available: the application you are trying to use is no longer available or access is limited.".

Users have no problems accessing with their existing Facebook accounts.

Answer: 
I get this issue when I create fake/test accounts on facebook. It seems like they take 1-2 hours to review the account before they will let you use the graphAPI.
If you just created a new business account, you will need to add one friend.