Does every protein starts with Methionine amino acid
No, not every protein starts with a methionine. When the methionine is removed, it is called N-terminal methionine excision. Abstract excerpt below:


  N-terminal methionine excision (NME) is the major proteolytic pathway
  responsible for the diversity of N-terminal  amino  acids  in 
  proteins.  Dedicated  NME components have been identified in all
  organisms, in all compartments  in  which  protein  synthesis  occurs:
  cytoplasm, plastids and mitochondria. Recent studies have revealed
  that NME is regulated at various levels and plays an important role in
  controlling protein turnover. NME is essential  in  Eubacteria  and 
  lower  eukaryotes  and  is  the target of many natural and synthetic
  inhibitors. Such inhibitors  have  considerable  potential  for  use 
  in the  treatment of various human diseases, from cancer to bacterial
  and parasitic infections.


And from a recent review focusing on the methionine aminopeptidase enzyme that cleaves the first methionine:


  Protein synthesis is initiated by methionine in eukaryotes and by
  formylmethionine in prokaryotes. N‐terminal methionine can be
  co‐translationally cleaved by the enzyme methionine aminopeptidase
  (MAP). When recombinant proteins are expressed in bacterial and
  mammalian expression systems, there is a simple universal rule that
  predicts whether the initiating methionine will be processed by MAP
  based on the size of the residue adjacent (penultimate) to the
  N‐methionine.


Mitochondria and other organelles also have different start codons. Their alternate start codons are well-characterized (AUA and AUU in humans and mainly - but not exclusively - GUG and UUG in prokaryotes).