John Carter passes on more info on the POP and IMAP question. "The reason you are able to see your mail on the server after seeing them using Mac Mail is that the preferences set in Mac Mail are to NOT remove the message from the server after retrieving them.
"In the snapshot below, I have my POP account preferences set to "remove copy from server after retrieving message” because in this case I have no interest to ever use webmail to access email for that account, and this option keeps the messages in that account on the server cleaned out.
"In this case, once I retrieve a message using Mac Mail (or any other mail app with the preferences set as above) and then subsequently either delete it from the inbox in Mail or move it to another folder in Mail, the message is deleted from the inbox on the server. Because it is not a POP account, when moving a message from the inbox to another folder in Mail the message on the server is just deleted. All folders in Mail for a POP account are local to the computer. And that’s another reason I prefer not to use a POP account if I can help it.
"(Note: the option to include - meaning to retrieve - when automatically checking for new messages is not checked because I have a filter for that account on that server to forward all incoming messages to another account on another server, after which they are automatically removed from the originating server. This may seem complicated, but it means I don’t have to check messages from multiple accounts.) For IMAP preferences, it’s also possible to keep messages on the server or not:
"The only need to keep messages on the server is if you would ever need to get to your email using webmail. I notice that one option is to keep only those messages that I’ve read, which seems backwards to me. I would think the option should be to remove the messages I’ve read and keep the ones I haven’t read (retrieved but not read). That’s the only confusing part that I can see here."
John concludes with, "The advantage of IMAP is that if you have two or more computers at home that you are using (like a laptop and a desktop) then both computers will always show exactly the same messages. Deleting a message on one computer deletes it from the other - unless the message you deleted was in a local folder. I never use local folders and I will use IMAP over POP (when possible) because I want my email on all my computers to be in perfect sync. That’s my personal choice. If you only have one computer then it doesn’t matter which protocol you use - although as mentioned in the previous note IMAP is more reliable and I think that eventually POP will go away."