Oh that's embarrassing, I also searched the Microstation help but I failed to see REFERENCE MERGE in "Miscellaneous References Key-ins" because it was collapsed. It is very easy to use help documentations if you are used to it, but it is difficult as a Microstation beginner. ;-)
Thank you very much, your explanations helped me a lot!
My final version if someone has the same problems:
1. Copy template file "TEMPLATE_CUSTOMER_XY.dgn to the destination folder: My.Computer.FileSystem.CopyFile()
2. Open design file: MicrostationApplication.OpenDesignFile()
3. Attach the exported dgn file from our CAE system: MicrostationApplication.ActiveModelReference.Attachments.AddCoincident1(<file_path_exported_file>, , "Logical_Export")
4. Merge reference into master (view 1) by logical name: MicrostationApplication.CadInputQueue.SendCommand("REFERENCE MERGE Logical_Export;MSELVIEW 1")
Regards