I don’t have a full answer but… Back in the day the Community Edition used to be featured on the official feature comparison overview. Now, bear with me because it has been quite a few years since I checked that out, but CE was basically a somewhat smaller version of the Modeler edition where some diagrams were not supported.
But in general: coping with a read-only diagram is a good indication that you’re using an unsupported feature.
Example: I’m using the modeler license myself (which I can seriously recommend) and when I open the provided example project I get access to a Decision Table (“Loan Approval”) under Business Modeling. But read only. If I then close the project, open the Diagram Navigator (View tab => Panes => Diagram Navigator) and then expand the Business Modeling node it becomes obvious: I only have access to the Business Process Diagram, Conversation Diagram, Data Flow Diagram, EPC Diagram, Process Map Diagram and the Organization Chart. No decision tables
Which is also my suggestion: open the diagram pane, expand the nodes and check the available diagrams. That will give you a clear indication what diagrams are supported and which not.
Hope this helps!