Proteins: Post translational modification
1) Is the attachment of zinc regarded as a type of post-translational
  modification?


It is not really considered a post-translational modification because the zinc atom is not covalently bound to the protein. Binding to zinc is adsorption.


  2) When carbonic anhydrase is denatured, is the zinc ion released in
  the medium?


Yes, but it depends on the extent of denaturation too. Metal ions can be removed using chelating ligands like EDTA, without actually denaturing the protein.


  3) Will the amino acid sequence (primary structure) be changed after
  denaturation? If yes, are amino acids removed after denaturation, if
  yes, which?


Denaturation does not include cleavage of covalent bonds. There won't be change in the amino acid sequence.


  4) I guess Zinc will be removed after denaturation. Is the remaining
  structure the primary protein structure?


Yes; just the polypeptide.