There are different rate limits, with different time periods. A basic answer is that it's 1 hour for failures and 1 week for successfully issued certificates.
More or less. You can check Certbot's logs in /var/log/letsencrypt. And all Let's Encrypt certificates are in public Certificate Transparency logs, which you can examine through an interface such as crt.sh:
I can't answer that. You can try to figure it out by examining the clients and logs on your computers. The Let's Encrypt staff could also examine the server logs, and they might chime in later in this thread. 
You can determine about when you'll next be able to issue another identical certificate from the information in the links above. For the rate limit in question, you can issue another identical certificate as soon as there haven't been 5 in the last week.
As the link above shows, something has been issuing (or trying to issue) identical certificates twice a day since June 26. 
You should have 12 valid certificates somewhere in /etc/letsencrypt or elsewhere on one of your computers.
(Actually, in a pinch, you only need one of the private keys. You can download the certificates again.)
You can work around the duplicate certificate rate limit by issuing a certificate for this name and one or more other names. (www.curted.com or another domain or whatever you'd like.) It sounds silly, but it will work.
Still, you need to figure out what's trying to issue so many certificates, and stop it.
Could you paste one of the recent log files from /var/log/letsencrypt?