Weird. Maybe you installed Houdini while Unreal was running? Not sure why a restart would fix it but glad it works now.
As for your questions:
1. In Unreal (or Houdini Engine in general) there is no difference between a SOP asset and an OBJ asset. OBJ assets are instantiated as-is in the root /obj/ and the parameters are parsed and displayed in Unreal. SOP assets are instantiated inside a dummy OBJ assets and the parameters of the SOP node itself get exposed (not the parameters of the dummy OBJ). Inputs for either OBJ or SOP appear in the inputs section.
2. Any SOP asset with a SOP input (or more) will have the input(s) be listed in the Input section above the parameters. You can drag a native Unreal mesh in there as input. For OBJ assets, HE looks for SOP Path type parameters and assumes those are geometry inputs and lists them under this Inputs section.