Hi Tim,
not all hp-functionality of NGSolve is wrapped to Python, yet. It will improve over the next weeks.
I just added the GetOrder function. You can query the order for each cell, face, and edge. Only isotropic order is supported (the C++ code supports anisotropic order as well). It will be in the upcoming nightly release.
To the second question: You cannot ask for the childs, but you can ask for the parent element: mesh.GetParentElement.
Best,
Joachim