Are you evaluating the API without license (e.g. temporary license)? Please note that there are trial limitations.
With the API license, we could successfully convert the use-case 1, 2.
We could not load the image inside the HTML at our end. Have a look at this screenshot.png (23.3 KB).
DCX to PDF conversion is not supported. We are getting following exception: Unhandled Exception: GroupDocs.Conversion.Exceptions.ConversionNotSupportedException: Conversion from to pdf is not supported.
Please avail the temporary license using these guidelines.