Aloha Nicholas,
I'm at work (on a Windows box

) so I'm going from memory, but to answer your questions, yes Mail can work with other than .Mac accounts. I, for example, use Road Runner. On one of the initial Mail setup screens, .Mac is the default selection, but if you click that button, you'll see other entries, such as POP, IMAP, etc... In my case, I chose POP, then entered my email address, pop and smtp server information, logon and password, then sat back and started working with Mail.
On the downloaded messages issue, look at Mail's preferences. Different email programs have different default actions with respect to downloaded messages. For example, Microsoft Outlook deletes all downloaded message from the server immediately upon the user downloading them. Mac's Mail, on the other hand, leaves them on the server for 10 days, if I remember correctly. There is a setting in Mail's preferences (I'll look it up after I get home, if no one has shown you where that is before then) that dictates Mail's default action. If, for example you set it to perform the same as Outlook, then once you download your mail messages to Mail, they are also deleted (removed) from the mail server. Then, when you check your mail again, you will no longer receive the message you previously thought were deleted as new messages.
I hope that will help you. Of course, if you need any further clarification or would like any additional information, please don't hesitate to let me know and I'll try to make it "as clear as mud."

Bud Jones
P.S. I've only had my iMac for 10 days, and I can already answer Mac-related questions - it feels great to provide some assistance to a fellow Mac user, considering how much assistance I've received