There’s no way to do it automatically. As I said above you can only import objects of the same type. So what I would do is create a “Meshes” folder inside the content browser and then open that folder and right click and choose import then select all of your FBX files and import them. If you want even more organization - for example you have Meshes - Architecture and Meshes - Nature, then you have to create those sub folders and import the appropriate meshes manually.
You can move files around by simply drag and dropping them inside the content browser, however if you do this after the files are being used (for example move a texture once its being referenced by a material) then it will move the file and update the location to its dependents but even if you empty out a folder, I’ve noticed that it still uses the folder as a reference.