Thank for the files: AI is indeed the wrong tool to create DXF content needs to be used by AutoCAD users. It appears the built-in translator in AI is making the conversions for you.

DXF files are just text files, open one up in your favorite word processor, circles do no exist in there. But there are lots of Splines. There is no conversion taking place inside AutoCAD with your DXF: that happened in AI's converter.

As noted, in AutoCAD the command REGEN or REGENALL will smooth out for Spline circular shapes so they do not appear too jagged. See below.

Not quite understanding the scaling issue unless your other recipient is INSERTing your DXF into a different-units-setting DWG file. AutoCAD has no preset units, a UNIT in a DWG file can be an inch, a mm, a mile, a lihtyear or a micro-whatever, the file creator makes that determination.