Mail: how to download newest first? Can I tell Mail to download the newest messages first? 

My Mac is my second computer. When I check e-mail, it has often been 2 weeks since I last opened Mail. Currently, I have to wait for hundreds of messages from 2 weeks ago to finish downloading before I can open that one message my client just now sent to me.
If you're using Mail to access your work email on an Exchange server, it's quite possible you'll be able to see the mail on Outlook Web Access (OWA).

To find out the address for OWA, check your Accounts preferences, and look for the "External Server" entry, simply point your browser to https://external.server.com (make sure it's HTTPS and not just HTTP) and you'll be able to login and view all the messages just like with webmail.