It's right to say coding sequence is part of exon sequence?
As I remember, exon sequences is the same with coding sequence, except
  for the first and last exon, which are parts of 5'UTR and 3'UTR,
  respectively, am I right?


Not necessarily. The UTRs can be composed of multiple exons and there can be an exon that spans both sides of the start codon i.e it is both a part of the 5'UTR and CDS. Similarly, an exon can span both sides of the stop codon.

A reason for why you are not able to map your repeat to any of the regions of the mRNA could be that your repeat falls in an exon that spans the start/stop codon. The repeat itself might span these sites. You need to provide additional details such as the location of the repeat, size of the repeat and which exon it maps to. Also mention which reference genome file are you using.