I'm looking at the SVG before it's converted to DXF. The missing letters are identified (both in status bar and XML Editor) as polygons.
In the DXF dialog (which maybe you just clicked through?) there are a few options. One is Use RoboMaster type of Spline output. And another is Use LWPOLYLINE type of output. It sounds like you maybe had both of them enabled, and the paths turned into Splines and the polygons turned into Polylines. I'm just guessing about that, I haven't actually tried it yet.
Ok, my first test will be with neither option enabled. Let's see what happens.... Aah, well all the text survives, at least in Inkscape. Note that I ungrouped everything first, before I saved as DXF. I'm not sure if that would matter or not. I only did that to make it easier to ID the objects (not because I thought it might help). Also, I did Not use Object to Path, although that probably would work as well.
There's some additional info on the Help tab of the DXF dialog, which might help you understand better.
The changing color may well be a bug. You're welcome to look into it, if you like. If it's not already reported, you can do it. Start here:
https://inkscape.org/contribute/report-bugs/But I don't think the missing paths is a bug, because it can be fixed just by using different options (or probably also with Object to Path). Although who knows, after playing around with all these various options, you might find a way to fix the color changing.
Just re-reading your original message. There might be a dialog for opening AI files in Inkscape (I don't have any for testing). And if there is, it might have some options that would affect this problem.