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I do not think that you can get all of that directly with sage.

A viable option would be to call mplot3d (plot_surface) from matplotlib, which is easily done in Sage. This way you can get point 1,2,4 even if the axis are displayed in a different way, and I think also point 3, but i am not sure about that. All the references are here.

If you need some kind of interpolation, I suggest you employ scipy.interpolate module. You can get many different types of N dimensional interpolation.