In general, you can store simple application settings and connection string in web.config (or app.config), but anything more complex, like an object graph or XML (as in your case) and you should consider a different method.
These may be helpful:
http://stackoverflow.com/questions/172646/how-do-i-store-an-xml-value-in-my-net-app-config-file
(it suggests encoding the XML in an app setting)
However it would be better to have a separate XML data file and convert it to an object graph using Linq-To-XML (see reference) or XPath and the XmlDocument and related classes.
Edit: see the other answer, which does allow XML in the config file. That's a more direct answer to your exact questions but I will leave this here for reference. On the whole it looks like your data is not configuration data (more like runtime / user data) and does not belong in a .config file: so I would recommend storing it in a separate XML file, and having a config file entry pointing to the filename of the separate XML file.
Hope that helps!