To whom did Hashem make this next statement?
Ramban #1: He said it either to the celestial beings in general who stood before Him to serve Him or to the angels who were currently doing His bidding (Refael and Gavriel).
Ramban #2 : The speech here refers to thought 1 - He thought (or decided) to inform him of what He was about to do, for the reasons that the Pasuk goes on to describe.
What was Hashem's quandary?
Targum Yonasan, Rashi and the Rashbam: It wasn't a quandary, it was a statement! He was saying that He could not possibly hide from Avraham what He was about to do to Sedom. Rashi explains how, having given him the land, including the five cities of Sedom, and having called him 'the father of a multitude of nations', how could He destroy the children without informing their father? In similar vein, the Rashbam points out how Hashem had given Avraham Eretz Yisrael, of which the five cities were part.
Why did Hashem see fit to divulge His plan to Avraham?
Seforno: He wanted to teach Avraham the principle of Teshuvah; that if there would be a number of Tzadikim in the town who might succeed in convincing the Resha'im to do Teshuvah, He would be willing to give them a chance (Tzedakah). 1 Otherwise, He would judge them (Mishpat). 2
Lev Eliyahu (Bereishis p.58): Because Avraham will command his children to do Tzedakah and Mishpat 3 , He should inform him, so he can teach them Derech Hashem, and do Tzedakah and Mishpat even wirth Resha'im. First he warns them; perhaps they will repent. Hashem is merciful and patient, even though their sin is very heavy. And they will know that a Tzadik must pray for Resha'im in his generation, like Avraham.
He would tilt the scales towards Chesed, because 'Hashem does not want the Resha'im to die.
Mishnas R. Aharon 1 p.20, Hagahah: After all the tests, Avraham had special dearness only because he will command his children, i.e. Zikuy ha'Rabim. This is the ultimate love. Only through this one merits the world to come. Without it, he receives the world to come only through Chesed Hashem. Lev Eliyahu (Bereishis p.55) - commanding his children also overrode the thousands and multitudes that he brought to know and serve Hashem. The Akeidah was so difficult, for through it he would lose this dearness!
Why does it say "and Hashem"?
Moshav Zekenim #1: This connects to the end of the previous verse. Because Avraham accompanied his guests and spoke Torah with them, the Shechinah rested on him.
Moshav Zekenim #2: This teaches that Avraham left the Shechinah in order to escort. We learn from here that we leave the Beis ha'Keneses or Beis Midrash to escort, for it is Piku'ach Nefesh.