I try to import a dwg file (using Projekt > DWG/DXF-Import) into QGIS (2.18.3 32Bit on Windows) which works quit nice.
Using FID field for managing your data is not proper since this column is filled in automatically by application. You can't delete or change that field, at least in most applications you shouldn't be able to.
Best way to handle your data would be to create new column with unique integer number, distinct for every feature. In AutoCAD you can copy it's original FID content to your new column. This way you will have ID property independent of application you are running.