Sure - you'll need create a user account for it and use authenticated SMTP, but there's no reason it wouldn't work.
In WSUS, Under Options->Email Notifications, this screen has all the configuration options you should need to set up sending through gmail. For details, see the "Outgoing Mail Server" section on this page. Also, don't forget to tick the "authentication" box and provide your username/password.
WSUS supports updates for Forefront antivirus from Microsoft for antivirus updates. As far as I know it does not support the downloading of 3rd party AV updates.
You obviously need WSUS setup on one of your servers. If you use Active Directory you can use Group Policies to apply the settings to your workstations.
If you do not have AD then you will have to make some registry changes. The best way to go about this is to make the changes on one machine, test it and then export the registry settings and import it on the other computers.
The instructions for GPO and the registry are here.
I don't believe so, but one workaround is to implement an intercepting proxy server on your network. This means that you can configure the WSUS server to instruct clients to download from Microsoft, but still cache the content locally for machines on your network. (As an added bonus, updates will only be downloaded if they are actually needed, so you can be less selective about what you approve.)
A variation of this is to configure WinHTTP on your desktop machines to use a proxy server, although this means laptops that are on-site will still download from Microsoft. In principle you could write some software that detects the current location of the machine and reconfigures WinHTTP as necessary.
Best Answer
Sure - you'll need create a user account for it and use authenticated SMTP, but there's no reason it wouldn't work.
In WSUS, Under Options->Email Notifications, this screen has all the configuration options you should need to set up sending through gmail. For details, see the "Outgoing Mail Server" section on this page. Also, don't forget to tick the "authentication" box and provide your username/password.