I have Outlook 2007 email on a notebook, can I access those emails through my new Outlook 2010 email account (same address) on another laptop?
Your Shaw accounts in Outlook will be using a POP setup, and therefor download emails from the server and store them on the hard drive of that computer. If you have each account setup to leave copies of messages on the server (this is an option in Outlook) then they will potentially be able to have the same contents, but there is no syncing possible between the two.
So the short answer is.. probably not. But there are ways to work around it. If you configure each account to leave copies on the server, then from here on out they will both receive the same emails (doesn't work backwards for emails you've already received). There's also the option of just forwarding yourself some emails if it's only a small amount that you want to be on the other computer.
Retrieving data ...