You can't put Texture on Sphere but we can create our own sphere :)

i = Import["http://jan.ucc.nau.edu/~rcb7/370moll.jpg"];

map = Colorize[(GeodesicDilation[  MorphologicalBinarize[#, {0.35, Automatic}], #, 3] &[i]), 
   ColorFunction -> "BlueGreenYellow"];

sphere = First @ SphericalPlot3D[1, {u, 0, Pi}, {v, 0, 2 Pi}, Mesh -> None,  TextureCoordinateFunction -> ({#5, 1 - #4} &), 
                                                      PerformanceGoal -> "Quality", PlotStyle -> Directive[Specularity[White, 10], Texture[map]], 
                                                       Lighting -> "Neutral", Axes -> False, RotationAction -> "Clip",  Boxed -> False]

You can find more explanation here: [...] projection onto a sphere?

Manipulate[
 Graphics3D[{Scale[sphere , {a, b, c}], Point@{0, 0, 0}}, PlotRange -> 2, 
  ClipPlanes -> {{0, -1, 0, 0}}, ClipPlanesStyle -> Opacity@.5], {a, 
  1, 2}, {b, 1, 2}, {c, 1, 2}]

Not sure how this is related to the topic, maybe you can use this:

Manipulate[
 Graphics3D[
  {Scale[Sphere[{0, 0, 0}, 1], {a, b, c}],
   Point@{0, 0, 0}}
  ,
  PlotRange -> 2, ClipPlanes -> {{0, 0, 1, 0}}, 
  ClipPlanesStyle -> Opacity@.5
  ]
 ,
 {a, 1, 2},
 {b, 1, 2},
 {c, 1, 2}
 ]

You can just write pts = Array[.... and than Graphics3D[ Point /@ pts]. Character % is the last output. Take a look at Out documentation.

You can switch to finite precission by N @ pts

About converting them to the list of triplets, you can do: Join @@ pts or Flatten[ pts, 1].

About exporting, probably Export["file.txt", Join@@pts, "Table"] or something like that, can't check now.

Good luck.

f[x_, y_] :=   If[x^2 + y^2 > 1, h = 0,    h = (Cos[(y \[Pi])/2] Cos[(x \[Pi])/2])^0.5];

Plot3D[f[x, y], {x, 2, -2}, {y, 2, -2}]

Extracting them may be complicated because those intersections are not calculated. Mesh lines are done for each direction separately.

But you can easily create them by yourself:

Array[{##, f[##]} &, {17, 17}, {{-2, 2}, {-2, 2}}]
Graphics3D[   Point /@ % ]

On the other hand you can extract actual plot polygons verices:

Plot3D[{If[x^2 + y^2 > 1, h = 0, 
   h = (Cos[(y \[Pi])/2] Cos[(x \[Pi])/2])^0.5]}, {x, 2, -2}, {y, 
  2, -2}, Mesh -> None, 
 PlotStyle -> Directive[EdgeForm[Thick], FaceForm@None]
 ]

% // Cases[#, GraphicsComplex[pts_, ___] :> pts] & // Short

{{{-2.,-2.,0.}, <<562>>,{<<1>>}}}

Or use V10 fancy stuff:

DiscretizeGraphics @  First @ Normal @    Plot3D[ f[x,y], {x, 2, -2}, {y,   2, -2}, Mesh -> None]

MeshCoordinates@% // Shallow

{{-1.85714,-1.85714,0.},{-1.71429,-2.,0.},{-1.71429,-1.71429,0.},{0.,-1.71429,0.},{-0.285714,-2.,0.},{0.,-2.,0.},{-1.42857,-1.71429,0.},{-1.42857,-2.,0.},{-1.14286,-1.71429,0.},{-1.14286,-2.,0.},<<554>>}