how transfer videos from within an App to the mac? I would like to know, if their is a way to transfer videos from Coursera-App on the ipad to the mac (without re-download them from the internet)?

I tried to connect the ipad through iTunes, to see if i can get the content of the app, but it seemed that I cannot get to the media inside the apps.
You can use an app such as iExplorer to copy the files over USB from the app's container.
iTunes File Sharing only works if the app in question supports this.