Think about it this way: a direct report of what the chap said in the then present would have had: "David Yurdiga said, 'It may be years before the city is running normally again' ". Now you could indeed say "will run normally" for this, but if you mean that it not only gets to a point of running normally but continues to do so beyond that point, then the present continuous is a better choice. Now use reported speech and put it in the past -- "may" becomes"might" and "is" becomes "was".

You are correct. News agencies are notorious for having grammar errors in articles. The original speaker may have been misquoted or he might have said it wrong.

Notice the word "said." That is a reporting verb, and it's in the past, so the indirect quotation it introduces is backshifted into the past as well. If the words quoted had been in past tense already, the indirect quotation would have used the past perfect. I didn't invent the language -- I just teach it :)