How to allow multiple authentication methods in ASP.NET?

I’m building a new ASP.NET MVC application (in C#) and one of the requirements is to create a new database of members. For this, we’d need roles to manage the different types of members and profiles to manage the additional metadata attached to each member. So far so good, just use the standard MembershipProvider, RoleProvider and ProfileProvider provided as part of the .NET Framework.

How to get the username of the user accessing ASP.NET intranet page within local network?

We have an ASP.NET intranet site, available to users who are either physically at and logged into a local machine or else to users who connect remotely via VPN. Is there a way to automatically get the username of whoever is accessing the page based on the name used to either log into the local machine or that used for the VPN?

ASP.NET WebForms Authentication Logout, Cookie can still be used to access site

I have been banging my head against the wall and searching the web for this but I think I am having issues understanding the whole process of logging users out of an asp.net webforms application. The issue:
I am able to log in to my application and it uses cookies, so I have my cookie set in the browser.
here is the config forms authentication section,