Hi Romain,
It seems that there might be some issue in your Studio account. Would you please contact Studio support to see if your account is set up properly to access the dynamic advertiser/profile?
In the mean time, can you try one more thing?
Please download my test file (from previous post) again, open it in GWD, then open the Dynamic dialog (double click on the binding in Dynamic Panel). It should open the "Bindings" tab in the dialog. Just don't go to "Data Schema" tab to change the advertiser/profile info. Instead, in the "Bindings" tab, try to add binding. I just wonder if you can add new binding in the test file? If it works, you can probably use the test file to continue adding content and bindings until the account access issue is resolved.
Thanks,
Emily
(Google Web Designer Team)