You can see the rate limits at Rate Limits - Let's Encrypt or summarized at Rate Limits for Let's Encrypt:
Renewal is essentially getting a new certificate, but it is an exact duplicate, so it is a "limit on issuing certificates with the exact same set of names: 5 certificates per FQDN set per week."
Yes, you can renew infinitely into the future, but not more than 5 times in any 7 day period. from the document you refer to
We also have a Duplicate Certificate limit of 5 certificates per week. A certificate is considered a duplicate of an earlier certificate if they contain the exact same set of hostnames, ignoring capitalization and ordering of hostnames. For instance, if you requested a certificate for the names [www.example.com, example.com], you could request four more certificates for [www.example.com, example.com] during the week. If you changed the set of names by adding [blog.example.com], you would be able to request additional certificates.
getssl will, by default, not renew if the certificate is valid for more than 30 days, so you can put that in a cron to renew every day, and it will only renew the cert every 60 days.