Interesting! I don't usually drag and drop files, but I could add fields to a CSV layer when I tried this. Which feels wrong :)
The changes weren't saved when I committed the changes. I could only get the changes to commit if I saved it as a new CSV file using save as... (Tested on QGIS 2.16.3)
I usually use CSV as a quick way of getting data from python scripts into QGIS, by writing WKT into a CSV. I have to use TAB or pipe (|) as a delimiter because WKT contains commas. If you drag-and-drop you don't get the option to set the delimiter and it assumes commas.
Take a look at the layer capabilities with the different scenarios (use Layer Properties > Metadata and scroll down the Properties section to look for Capabilities)
If you import a delimited layer (with geometry) you should see...
Create Spatial Index, Fast Access to Features at ID, Curved Geometries
If I drag in a CSV file, or import one without a geometry, I see
Add Features
Notice that in both cases, there isn't an "Add attributes" capability. This might explain why I need to save as a new CSV.
The GDAL/OGR CSV driver doesn't allow in-place edits (no 'Add features' or 'Add attributes' capabilities).
I suspect that when you drag in a CSV file without a geometry, QGIS treats it as a text file. If you import a csv and the geometry is recognised, the GDAL/OGR driver is used, and it won't let you make edits.
I created a simple script that generates the Javascript definition of the GEE points starting from a csv file:
https://github.com/lucamarini22/csv_to_gee_points
In particular, given a csv with at least 2 columns containing respectively the latitude and longitude coords, the scripts generates the definition of all the points that can be then inserted in the Code Editor of Google Earth Engine.
Best Answer
The problem is occurring because of the CSV file you're using. The column headings will have spaces and/or illegal characters within it, which is why it is not being displayed correctly on the event layer. You need to edit these within the CSV.
Please see this link about field characters within arcmap.