Attempting to export a mesh to another 3d App- yet both Alembic and FBX exports yield files with no data. I have Houdini Indie- why would a basic mesh not export to either Alembic or FBX?

If you middle click on the File node that brings in the Moon you will notice that there is no actual mesh geometry in your scene. What you are looking at in the viewport appears to be volumes. Alembic and FBX can not contain volume data, that is one reason why .bgeo.sc is so nice, it can contain volumes and attributes.

Drop down a Convert node after the File and connect them. Then middle click on the Convert and you will see that you have actual polygons.

Move the Display flag to the Convert node then try your export again.