Live Mesh storage: You should make (after searching for/voting on) a suggestion on
Connect. It's not a bad idea, though I believe it's going to be up to the Live Mesh team to provide the functionality you're looking for.
Remote Desktop: The Windows Home Server team uses the Remote Web Workplace functionality built in to Small Business Server. That requires remote desktop support on the clients for RDP proxying to work. Live Mesh works by having every PC with the software installed "phone home" to a server in the cloud on a regular basis (probably fairly frequent). This is required because of how Remote Assistance works; the Remote Desktop connection you're making from your PC at work through Live Mesh is initiated by the PC you're connecting to. If that PC didn't contact the Live Mesh servers, it wouldn't know to initiate the connection. (The actual handshake is rather more complex than that; I think there's some documentation on it on the Microsoft Support or TechNet web site.) I think the RWW (i.e. WHS) methodology is a bit more secure/robust, personally.