Yes, the bnconfig tool configures some values in the database but if it seems it's not needed as your site works properly after the change.
I'm not aware of any issue when using a CNAME but this is a question for the Let's Encrypt community.
No, no change is needed
If you are not going to use mini.example.com, I'd remove the entry in the cron file to not to renew that certificate. Please note that the webserver needs to be stopped every time you want to renew a certificate.
This online tool shows the status of the propagation
I'm glad to hear that everything is working properly now!! Enjoy the application