I have attached the DXF file in question, as well as the AI file. This is exported from AI with the settings you see above. 

Does anyone have the ability to open it in AutoCAD and see smooth arcs around perimeter of pieces and also perfect circles?

One of the most important features of AutoCAD is the use of DXF files. DXF is very important standard in the entire vector wold. The only reason i'm talking thoroughly about AI is to show that i have done nothing wrong in the export.

If autoCAD can't interpret a DXF correctly or is causing issues, then this is something that AutoCAD's team needs to be aware of. And with my case here, it is entirely possible that this is an AutoCAD error. I can not conclude that yet, but lets try to figure this out.

thanks