You don't need Office 2007 to use Office Live. You get some cool integration of features like two way sync with Outlook Calendar and Task items, but you can use Office Live stand alone too...
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Well, you can access Office Live web services, but not create your own. Click here for a list of the Web Services that Office Live provides.
The endpoint or URL of the web service depends what Office Live bizapp or workspace you are trying to connect to. Just navigate to the Bizapp in question and look at the URL in the browser. Copy and paste the root of the URL and tack on the web service portion at the end.
Each Bizapp is it’s own subweb, so most of the URLs in question will look something like this:
https://<yourdomain>.officelive.com/<subweb name>/_ vti_bin/Service_Name.asmx
You can also access external web services using the Data View web part, as Albert shows in the screencast.