After the reader finishes the Book, he says Chazak Chazak v’Nitchazayk. The congregation responds in same. Then, does the reader repeat the last Pasuk?

The Rema OC 139; 11 writes that from the verse in Yehoshua 1; 7 " Strengthen yourself and persevere very much to do according to all the Torah…" the custom is to say Chazak to the Oleh that finishes a book. The Levush writes – and that is the Ashkenazi custom – to say "Chazak Chazak Venitchazak". The Aruch Hashulchan says that the words should be Chazak Chazak Chazak" since this has the same numeric value of the word Moshe. The Achronim bring that since it is a blessing of strength to the person that got the last Aliya – he should not recite the verse for he should not bless himself (Proverbs 27; 2) and so there will be no interruption between his reading and the last Bracha for the Torah. In any event the common custom is that the reader ends the reading in a different tune and all recite "Chazak Chazak Venitchzak", only then in response to the congregation the reader himself recites these words aloud.