In Azure on Subscription level I have **Azure Data Factory Contributor **Role and on the Resource Group I'm the owner. With this permission set I still can't create an Azure Data Factory in the Resource Group. What role/permission do I miss? It looks like after a first creation of ADF with this rol we can create it.. So what is initially needed to create ADF?
Error:

add permissions on subscription level, but without any result. Can't ask for Admin rights on subscription. Looking for a minimum permission to create ADF in a Resource Group

Azure Data Factory Contributor Role will just allow you to create and manage child resources for ADF like dataset linked service.
To create Azure data factory instance, you need
Owner,Contributororadministratorrole at the Azure subscription level to the user with which you are signed in.For better understanding refer this MS Document