Thanks!
Yeah, some of the trophies are probably hard -- the times are based on a computer solver, who sometimes finds ways to cut off time that I was not expecting. (Although a few seconds over the solver's solution are allowed.)
Nil is homogeneous (the same at every reference point) but anisotropic (not the same in every direction). Although it is rotationally symmetric (the up/down direction is special, but you can rotate around this axis).
No idea about actual planets :) I do not think anybody has studied that.