How to save the postprocessing data
 

Is there a way to store the data in some kind of file format? e.g. Mesh data?

You can save from within parav
 

You can save from within paraview2.2 the currently selected data as -I think - a .pvd file which is the xml based vtk format.

There is no tool to read this back into OpenFOAM, either as a mesh or as a field. Would be quite interesting though to be able to do this...