I think the incorrectly detected card is because Skyrim doesn't know anything about Mac/Linux drivers, and so makes its best guess based on the output it sees, and is always wrong.
The limitations you're experiencing are almost certainly more of the same - Skyrim (and games like it) pass a lot of very complex d3d code that we translate to openGL and feed to the driver. Some drivers have better openGL support than others, and unlike native apps which can adjust to dropped/unavailable openGL extensions, when extensions fed by Crossover are dropped or unhandled by your driver, Skyrim doesn't know how to deal with the feedback and the end result is more instability/glitches/etc.
The fact that you can play Skyrim, at all, implies that cancelling the re-install of DirectX and .NET didn't really do any harm. In my own testing when I've cancelled these steps out of impatience the game just didn't launch. I'm honestly not sure about how to force those installs, again, short of blowing away the game files in steam and re-installing (which of course will take forever).