I lost all my Youtube favorited videos because iOS 6 doesn't have Youtube anymore. Can I switch back to iOS5?

Well, you can just find YouTube on your web browser, once done then open the square with arrow in it same as you would add a bookmark, you now have option to place to home screen, this creates a app icon so this way you will press and be sent straight to YouTube. It's not the same but it's the same.

Hope this helps...

You can find all of your favorites in the safari browser, under bookmarks. Still not integrated into the app, but there they are.