I have Luma CFW and the version 11.15.0-47E firmware. The card works fine with my CFW old 3ds.
I am pretty sure they do not but in any case Luma CFW bypasses the flash cart blacklisting which means any cart will work except ones that rely on the original DS boot sequence like the original R4 but even those can be booted with a Stage2 launcher. In otherwords, if it worked on DSi or 3DS firmware 1.0.0 it will work with Luma.
That being said, the DSTwo is known to have issues with fitting and making contact properly because it is thicker than other carts so it is most likely a physical issue, not a firmware issue.