Regardless of the output format, you need to expose the following two format attributes in the DGN reader: "fme_basename" = dgn filename (without the extension), and "igds_level_name" = the layer name. If you need the full filename with path, you need to expose "fme_dataset" as well.
You can e.g. use the AttributeManager to rename them before output.
Use the GeometryFilter to only retain the line geometries.
You can select multiple folders or directories for your dgn files like this, that way you don't have to use any additional functionality:
For example, this will read all the *.dgn files in any subdirectory under C:\Temp
C:\Temp\**\*.dgn