Aizatulin

Here are some modifications (with explanations) of your file.

You can workaround the flat grid problem by extruding it (it is not nice but is working). Regarding to the angle problem, I have no other idea at the moment than to map every angle onto a different scale factor (using a ramp or a there is probably a function). But I don't know how to apply different scale factors in one bevel node. Using a feedbackloop, where you set for each iteration a group for each single edge.
Here is another file

@edit: it seems that tangent (x -> tan(x)) is doing the job (check the other file)

You can use a second input of the bevel with a profile curve generating a superellipse by a parametric formula. It seems to give quite acceptable result, if you set convexity to zero and scale factor to 2.
Here is an example file