Hi Jeff Sodeman,
Sitefinity can work with standard ASP.NET Membership, Role and Profile providers.
1) Prevent anonymous access to Sitefinity, and have non-logged in users redirected to the existing app's login page
Each page has a permission tab from where you could disable Anonymous access and allow only authenticated users to access it. If the user is not authenticated he/she will be redirected to loginUrl
of FormsAuthentication node.
2) Link from the existing app to Sitefinity and have logged in users be able to view SF without logging in again
You have to implement SSO with Forms Authentication or log in the user or create a "fake" login
3) Keep the SF cms admin users separate
You can use Roles model ( standard for ASP.NET) or 2 or more providers where one of them will be used only for the backend. Note that out of the box you can access the backend(admin) using only one Membership/Role provider.
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