how Wep API works together with ASP.NET MVC 5

I developed a website using ASP.NET MVC5 with Entity Framework and Microsoft Identity. Now I need to add Web API to this project for mobile app development using RESTful architecture. My questions are:

1. does Api controller and Mvc controller shares the same request pipeline?
2. can i separately implement the Cookie based authentication for website and the Token based authentication for Api?
3. if I deploy the website on IIS, does this mean Web Api will also be automatically hosted by IIS?