How can I run the Control Panel from a separate domain?
You can use the baseCpUrl config setting to tell Craft to always generate CP URLs pointing to http://admin.domain.com, and you can create a .htaccess redirect on http://domain.com pointing all requests to /admin* to http://admin.domain.com/admin/*, but it is not currently possible to get rid of the CP Trigger segment at this time. Craft relies on that to determine if the current request is a CP request.