Gemara

(Mishnah): We do not protest against Nochrim who take Leket, Shichechah and Pe'ah. This is an enactment for Darchei (for the sake of) Shalom.

(Beraisa): We finance poor Nochrim along with poor Yisre'elim, we visit sick Nochrim along with sick Yisre'elim, and we bury Nochrim with Yisre'elim. All these are for Darchei Shalom.

Avodah Zarah 20a (Beraisa): "V'Lo Sechanem" - do not give to Nochrim Chinam (free gifts).

(Beraisa - R. Meir): "Do not eat any Neveilah; to a Ger give it and he will eat it, or sell it to a Nochri" - one may give or sell it to a Ger or Nochri.

R. Yehudah permits only what the Torah explicitly says, i.e. giving it to a Ger or selling it to a Nochri.

Rishonim

The Rif and Rosh (28a and 5:23) bring the Mishnah and Beraisa in Gitin.

Ran (DH Kovrim): We do all these matters for Darchei Shalom not only amidst doing them for Yisre'elim. A Tosefta teaches that we eulogize Nochrim and console their mourners (even though we are not engaged with Yisre'elim at the time). The Yerushalmi does not say 'with Yisre'elim' regarding any of these matters. We do not bury Nochrim near Yisre'elim, for we do not bury Resha'im near Tzadikim. Rather, we engage with them to bury their dead.

Rambam (Hilchos Matanos Aniyim 7:7): We finance and clothe poor Nochrim along with poor Yisre'elim, for Darchei Shalom.

Rambam (Hilchos Avodah Zarah 10:5): We finance poor Nochrim along with poor Yisre'elim, for Darchei Shalom. We do not protest against Nochrim who take Leket, Shichechah and Pe'ah, due to Darchei Shalom. She'elas (inquiring about) Shalom of Nochrim is permitted even on the day of their festival.

Rambam (6): All these apply when Yisrael are exiled among the nations. When Yisrael has the upper hand, we may not leave a Nochri idolater among us. He may not even dwell temporarily or pass through our land from place to place for business until he accepts the seven Mitzvos of Bnei No'ach (and becomes a Ger Toshav) - "Lo Yeshvu v'Artzecha."

Rebuttal (Ra'avad): We never find this. The verse he brings applies to the seven Kana'ani nations, and even regarding them it forbids only dwelling, not passing through.

Kesef Mishneh: The Rambam holds that since the Isur is lest we be drawn to sin, the same applies to passing through, temporary dwelling, and to all Nochrim.

Rambam (Hilchos Melachim 10:12): Chachamim commanded to visit sick Nochrim along with sick Yisre'elim, bury their dead with dead Yisre'elim, and to finance poor Nochrim amidst poor Yisre'elim, for Darchei Shalom. It says "Tov Hash-m la'Kol v'Rachamav Al Kol Ma'asav" and "Deracheha Darchei No'am v'Chol Nesivoseha Shalom."

Rambam (Hilchos Evel 14:12): We bury dead Nochrim, console Nochri mourners and visit sick Nochrim for Darchei Shalom.

Rosh (ibid.): We console Nochri mourners for Darchei Shalom. A Tosefta teaches that we eulogize Nochrim for Darchei Shalom.

Question: R. Yehudah forbids giving free gifts to Nochrim. Does he argue with the enactment to finance poor Nochrim for Darchei Shalom?

Answer (Tosfos Eruvin 46b DH Rebbi): Darchei Shalom is not called a free gift.

Poskim

Shulchan Aruch (YD 151:12): We finance poor Nochrim, visit their sick, bury their dead, eulogize them and console their mourners, for Darchei Shalom.

Bach (DH v'Chen): The Tur relied on the Tosefta, which the Rosh brought, to permit all of these Stam, even not amidst Yisre'elim. The Rambam distinguishes. He wrote that we finance their poor only amidst poor Yisre'elim, but did not stipulate (in Hilchos Evel) so regarding burying their dead, consoling their mourners and visiting their sick. However, in Hilchos Melachim he said that we bury dead Nochrim with dead Yisre'elim! It seems that this teaches that if Nochrim were found dead with Yisre'elim, we may bury them in the same Chatzer, for Darchei Shalom. Surely we do not bury them next to Yisre'elim. We do not bury even a Rasha Yisrael next to a (Kosher) Yisrael! Tosfos connotes that Darchei Shalom applies even to Tzedakah even not among Yisrael, if they were travelling together. The custom is to finance poor Nochrim even not amidst poor Yisre'elim.

Taz (9): The Maharshal says that the Gemara was not precise when it said with Yisre'elim. This is difficult. Rather, the Mishnah said that we do not protest against Nochrim who take Leket, Shichechah and Pe'ah, without mentioning 'with Yisrael.' In every case we do so even without Yisre'elim. One who returns an Aveidah to a Nochri transgresses, for he equates him to a Yisrael, and shows that Mitzvos are not dear to him, for he does the same even without a Mitzvah. The Beraisa said 'with Yisrael' to permit doing for Nochrim these matters of Darchei Shalom the same way we do for Yisrael. They are unlike Hashavas Aveidah.

Ri Korkus (Hilchos Matanos Aniyim 7:7): In every case we do only what is needed for Darchei Shalom, to avoid enmity. Normally, there is enmity only when we do these matters only for Yisre'elim, but not for Nochrim.

Rema (251:1): We finance poor Nochrim amidst poor Yisre'elim, for Darchei Shalom.

Shach (2): Really, we do so even when there are only poor Nochrim, like the Ran says. The Darchei Moshe cites the Ran.

Rebuttal (Gra 2 and Drishah 1): No, the Rema rules like the Mordechai (464), who says that we do so only amidst poor Yisre'elim. (The Darchei Moshe cited both opinions.) The Shulchan Aruch (151:12) rules like the Ran.

Shulchan Aruch (335:9): We visit sick Nochrim for Darchei Shalom

Shach (8) and Gra (12): This is even if there are no sick Yisre'elim with them.

Shulchan Aruch (367:1): We bury dead Nochrim and console their mourners for Darchei Shalom.

Kolbo (cited in Beis Yosef DH Kosav): One who sees a Mes must stand and show honor. One must accompany even a Nochri four Amos. This is astounding, for in Nidah (Chidushei Hagahos - Agadata) we say that if Shimon slaughters for a Nochri and eats with him, if Shimon dies we do not follow his bier. All the more so one need not follow a Nochri's bier!

Beis Yosef (ibid.): This is not difficult. A Yisrael Rasha is worse than a Nochri! The question does not even begin, for we accompany Nochri Mesim for Darchei Shalom. However, perhaps this is only for righteous Nochrim, who have a share in the world to come.

Bach (DH Kosav): The Beraisa listed things we do for Nochrim for Darchei Shalom. The same applies to everything similar. Even though a Nochri is worse than a Yisrael Rasha, one must accompany him so we will have Shalom with Nochrim.

Shulchan Aruch (CM 249:2): One may not give a gift to a Nochri who is not a Ger Toshav unless he knows him, or if it is for Darchei Shalom.