A trial version can be installed on as many computers as you want, but it will eventually time out. You could install only the parts of Office 2007 you want, and then follow it up with an install of your Office 2010 version.
You re-asked the same question about your e-mail without giving the most crucial and necessary detail. How is your e-mail currently configured? POP3, IMAP, or Exchange? What service do you use for your e-mail? Unless you use IMAP or Exchange, you aren't going to be syncing them easily. You can with a POP3 account, but you would have to configure Outlook to leave a copy of the e-mails on the server. It is cumbersome, but it works. It also doesn't sync all messages, either, so I would switch to IMAP or find a web-based service, like Gmail to handle your existing accounts.