Question: I am just getting started using QGIS 3.6.3. I added a Google satelite imagery using QuickMapServices, which is projected using EPSG:3857 - WGS84/Pseudo-Mercator. Then, while importing some points in a .csv file, I thought that I should choose the same CRS so it lines up with the basemap. But that puts my data on the other side of the world. When I select ESPG:4326 - WGS 84, it lines up whith the basemap.

Are coordinates taken with an handheld GPS device inherently saved in ESPG:4326 and then reprojected when added to a Google EPSG:3857 - WGS84/Pseudo-Mercator basemap?

Answer: 
Short answer is no. EPSG:4326 is used by default in GPS devices, but most devices have option to change the reference system. In that case, the data will be in the set reference system. 

When you add the data in QGIS, it will reproject the data in any known reference system to the map's projection system (in this case EPSG:3857)
As a rough rule of thumb, yes, must consumer GPS devices (especially Garmin) will default to WGS84, and it tends to be a safe assumption that a shapefile or other spatial data without a defined CRS is likely in WGS84, even in industrial/agricultural settings.

On some devices, you can explicitly set the CRS used for the saved data, but without knowing what hardware you're using, I can't help you more that way.

In general terms, yes, QGIS will do on the fly CRS/GRS transformation unless you explicitly disable it/change it from the default behavior.