Okay, let's try this.
Please "tail" (follow) the mail log and copy only the messages that occur at the precise moment when you get the above-pictured error message. To tail:
tail -f -n 30 /var/log/mail.log
As for the Evolution configuration, is pressing that "Check for supported types" button a requirement? If not, can you just ignore it?
I use Thunderbird and it can't pass that step automatically, either (I'm not sure why), but when I tell it which authentication mechanism to use, explicitly, it works fine.
Regarding the mail subdomains, it is a standard convention to use mail.example.com for POP/IMAP/SMTP, but there's no technical reason for which you can't forego convention and use that domain for webmail instead. (The convention for webmail is usually webmail.domain.com.)
Truth be told, all of those domains are likely to resolve to the same IP address, so it wouldn't matter which one you actually used.
And yes, that's correct: you can create as many subdomains as you like once you control the TLD (top-level domain).