1)
Why does the Torah need to mention here that Lot was Avraham's nephew?
1.
Seforno: The four kings made a special effort to capture Lot precisely because he was Avraham's nephew, and they assumed that Avraham, who was extremely wealthy, would pay a handsome price for his release.
2.
Chochmah u'Musar (Vol. 2, p. 370): The phrases "they took," and, "he was dwelling in Sedom," are also extra. By natural means, it would be unlikely that they would be able to capture Avraham's nephew, whom Avraham had taught and trained. What caused this? He dwelled in Sedom.
2)
Why does the Torah see fit to remind us that Lot lived in Sedom?