I am aware of this tutorials
http://wix.tramontana.co.hu/tutorial/getting-started/putting-it-to-use
http://www.codeproject.com/KB/install/WixTutorial.aspx
… but I can’t find a quick solution for installing web sites and configuring IIS.
Is it necessary to manually add each file of the site?
You don’t need to add each file manually. Instead, you can use Paraffin to harvest the files needed from your web project.
I configured it so that it is automatically run during a build (local or on the server) by manually modifying the Wix project file to add a BeforeBuild action. Here is an example, you can use this as a starting point.