In which circumstances are suitable for Web Application or Web Site in Visual Studio?

I have one project which has APP_CODE folder and runs with Windows Authentication.

1) I created Web Site and added the files of project but I couldn't run with windows authentication

2) Then I created web application project and check "Use Visual Studio Development Server". But now, I couldn't get access to the classes which are in App_Code folder.

There is no choice to select Visual Studio Development Server when I use Web Site project!

Questions:

1. Why can't I add APP_CODE folder to the Web Application ?
2. Why can't I run my Web Application on Visual Studio Development Server?
3. In which circumstances I should choose Web Site or Web Application options ?

PS: I want to put pictures of Web Application and Web Site:

Web Application:

Web Site: