These parameters refer to Grasshopper Groups not Rhino Groups.

In "native" Grasshopper there is only the ability to bring in the the objects that make up a group separately. i.e if you have a curves and surfaces and polysurfaces etc. then you would need Curve Param and Srf Param and BRep Param.

However there is an alternative way which uses the Geometry Pipeline component. This allows you to specify an objects name and it will reference anything in Rhino with that name (or mask). It also does layers. There is a filter on the component so you would need to make sure each of your geometry types is enabled. From the Pipeline you can then connect them to a Group Component located in the Transform Tab > Util Panel

Try the following definition. It will display the groups contained in the Rhino document, you can then select the one you want. If you input a list of group names instead of a single one it will output the objects of each group in a different branch.

You don't need to type anything in the Pipeline component, its just there to (very inefficiently) update the groups when you make changes.