Why does the Torah insert "Ki Li B'nei Yisrael Avadim"?
Rashi #1: To teach us that Hashem's document of sale (purchasing Yisrael as Avadim) preceded that of the Nochri.
Ramban and Moshav Zekenim (both in Pasuk 47): Even though the Nochri is not subject to the Dinim of Yovel, he does not have the authority to buy Hashem's servants as slaves.
Targum Yonasan: Yisrael are Hashem's Avadim in that they are subservient to His Torah, and may not be enslaved by others. 2
Refer to 25:55:2:3.
Bava Kama, 116: To teach us that a hired worker can retract in the middle of the day 3 - since 'Yisrael are Hashem's servants and not the servants of servants'.
Why does the Torah insert "Ani Hashem Elokeichem" here?
Rashi: To teach us that whoever enslaves Yisrael on earth, it is as if he has enslaved them above. 1
Seforno: To teach us why Hashem will redeem Yisrael even if they lack Mitzvos. 2
Da'as Zekenim: The Pasuk continues "Lo Sa'asu lachem Elilim," as if to say - at least they fulfilled "Lo Yih'yeh l'cha Elohim Acherim", which is why Hashem redeems them even though they do not fulfil the Mitzvos.
The Gemara in Bava Metzi'a 10a learns from "Ki Li B'nei Yisrael Avadim" that a worker can quit in the middle of the day. Why do we need "Vefefdah" to teach us that one may redeem an Amah Ivriyah?
Moshav Zekenim (citing the Ri): There, the Torah fixed six year of servitude. One might have thought that she cannot leave until they finish.
Refer to Sh'mos 21:8:151:1-3 & 21:8:152:1-4.
Why does the Pasuk begin in the third person ("Ki Li B'nei Yisrael?") and end in the second person ("Ani Hashem Elokeichem")?
Moshav Zekenim: Most Pesukim that discuss Yetzi'as Egypt follow the same format, because there were some in Goshen,and some in Tzo'an, the capital with B'nei Efrayim and Menasheh. 1 Sometimes it discusses Yisrael, and sometimes the Erev Rav. "Ki Li B'nei Yisrael Avadim" discusses those in all Mitzrayim) and "Ani Hashem Elokeichem" discusses those with Par'oh in Tzo'an.
He assumes that Yosef's descendants remained in the capital. I do not know his source. (PF)