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If you have a windows environment and all of your computers are joined to your domain you can use the remote assistance tools built into windows as long as the machine you are using to connect to client with is running Windows 7.
http://technet.microsoft.com/en-us/library/ee126163%28WS.10%29.aspx A quick shortcut to run RA in offer mode is "msra.exe /offerra"
Yes and no.
If your clients use an active VPN to connect back into the district than things would work exactly as they do on the domain. If they don't then you would need to use the "Email a link" feature which is client initiated and will work in most situations but you are at the mercy of firewall configs, etc.
In regards to the Email a link feature, I've found that in most circumstances, it will fail. People are behind all sorts of routers, and firewalls at home. And of those cases, nobody has a clue on how to allow this service to get through.