Spatially joining polygon fields onto point layer in QGIS?

The best tool for this job in my experience is Add polygon attributes to points in the Processing toolbox. If it does not work directly with the CSV, just save the points to a Shapefile before you run the spatial join.

Processing > Toolbox > SAGA > Vector point tools > Add polygon attributes to points:

Then you select the attribute from polygon data to add:

You can repeat the process with the result to add more than one attribute.