Hi Thomas,
Regarding the deformation question: The bilinear form has to be reassembled for the mesh deformation to take effect. Whether mesh retains its quality after the deformation depends on the quality/size of the deformation. The deformation computed for higher-order level set approximations is small, so in that case, the mesh quality is fine after the deformation.
I am not aware of a fast marching algorithm implemented in NGSolve/ngsxfem.
Best wishes,
Henry