Problem A: Produce your own parametrized surface. You can use any tool. Here are some ideas: Mathematica Notebook. 
picture = Import["http://www.courses.fas.harvard.edu/~math21a/exhibits/lissajoux/donald.jpg"];
ParametricPlot3D[(2+Sin[t]) {Cos[t] Sin[s], Sin[t] Sin[s],Cos[s]},
  {s,0,Pi},{t,0,2Pi}, Lighting -> "Neutral", Mesh -> False, PlotPoints->40, 
  TextureCoordinateFunction -> ({#5, #4} &), PlotStyle -> {Texture[picture]},
  ViewPoint -> {-3.25,-0.9,-0.2},ViewVertical->{-0.64,-0.05,-0.9},
  Axes -> False, Boxed -> False, PlotRange->All]


f[t_] := {Sin[t], Sin[3 t], Sin[2 t]}; 
ParametricPlot3D[f[t]+f[s], {t,0,2Pi}, {s,0,2Pi},
 TextureCoordinateFunction -> ({#4,#5} &), AspectRatio -> 1,
 PlotStyle -> Directive[Texture[ExampleData[{"ColorTexture", "Metal1"}]]],
 ViewPoint->{-1.8,-2.6,-1.17},ViewVertical->{-1,0,-0.1},PlotPoints->100,
 AspectRatio->1,Boxed->False,Mesh-> False, Axes -> False];
If you should not have Mathematica ready, don't sweat it. Here are some online tools, with which you can solve Problem A too: Render a surface of your choice and print it out.