Why did Avraham mention specifically fifty, forty, thirty, twenty and ten Tzadikim?
Rashi and Targum Yonasan: Because that would mean ten for each of the five towns (Sedom, Amorah, Admah, Tzevoyim and Zo'ar), four, three, two or one, respectively.
Why does Avraham, both here ("in the midst of the city") and in Pasuk 26, refer exclusively to Sedom?
Rashi, Seforno and Rashbam: Because Sedom was the metropolis 1 (Rashi Pasuk 26) and the king of Sedom chief of the kings (Rashbam).
Ramban: (citing the Ibn Ezra): Avraham mentioned "in the midst of the town" because the people feared Hashem in public.
Ramban: He mentioned it, because he thought that Sedom might perhaps be worthy of salvation on account of the temporary residents who lived there, such as Lot (and maybe there were others like him).
The Seforno add that Hashem specifically mentioned Sedom because that is where the cream of the crop gathered, and where the righteous people who would rebuke the Resha'im would be most likely to be.
Why does the Pasuk switch from "Lecha" (masculine) to "Lach" (feminine) in the same Pasuk?
רש"י: עשרה צדיקים לכל כרך וכרך, כי חמשה מקומות יש: בפסוק כתוב "בתוך העיר", משמע שדיבר רק על סדום?
גור אריה: סדום היא העיקר והשאר טפלים לה ומצורפים אליה.