Gemara

(Beraisa - R. Meir): "Lo Sochlu Chol Neveilah la'Ger Asher bi'Sh'arecha Titnenah va'Achalah Oh Machor l'Nochri" permits giving [a Neveilah for free] to a Ger (Toshav, i.e. a Ben Noach who accepted to observe his Mitzvos) and selling it to a Nochri (idolater).

"La'Ger... Titnenah... Oh Machor" permits selling it to a Ger.

"Titnenah va'Achalah Oh Machor l'Nochri" permits giving it to a Nochri.

R. Yehudah permits only like the Torah says, either a gift to a Ger or a sale to a Nochri.

He holds that had the Torah meant like R. Meir, it should have said 'la'Ger... Titnenah... u'Machor'. Rather, "Oh Machor" teaches that one may do only like [one of the two ways that] the Torah [explicitly] said.

R. Meir uses "Oh" to teach that a gift to a Ger is better than selling it to a Nochri.

R. Yehudah already knows this, since we are commanded to support a Ger, but not a Nochri.

22a - Question (R. Yitzchak Nafcha): Regarding Gid ha'Nasheh it says "Lo Yochlu... Es Gid ha'Nasheh." (R. Avahu should forbid benefit from it!)

(Mishnah): Reuven may send a thigh to a Nochri with the Gid ha'Nasheh inside. (The Nochri will show more appreciation for receiving a nicer thigh. Reuven benefits from the Gid!)

Answer: When the Torah permitted [to give to a Ger] a Nevelah, this permits benefit from [every edible part, including] the Gid.

This is like the opinion that the Gid has taste (R. Yehudah).

Avodah Zarah 20a (R. Yosi b'Rebbi Chanina): "V'Lo Sechanem" forbids giving to Nochrim Chaniyah (a place to stay) in Eretz Yisrael.

The Torah could have written 'Lo Sechunam' to teach this. Rather, it says "v'Lo Sechanem" to forbid also giving to them Chen (praise).

It could have written 'Lo Sechinam' to teach these two laws. Rather, it says "v'Lo Sechanem" to forbid also giving to them Chinam (a free gift)!

Gitin 40a (Rav Dimi): If a man said before he died that his heirs should not make his Shifchah work, we force them to free her.

Objection (R. Ami and R. Asi): [If she is not freed,] her children are slaves. Why must the heirs free her?

(Rav Shmuel bar Yehudah): If one said before he died 'my Shifchah made me happy. My heirs should make her happy', we force them to make her happy.

This is because it is a Mitzvah to fulfill the request of the deceased.

61a (Beraisa): We finance poor Nochrim along with poor Yisre'elim, for Darchei Shalom.

Eruvin 64b (Beraisa): Once, R. Gamliel was on the road with R. Ilai. R. Gamliel found buns, and told R. Ilai to pick them up. He encountered a Nochri, and said 'Mavgai, take the buns from Ilai.'

R. Ilai talked to the Nochri. He found that his name was Mavgai, and that R. Gamliel did not know him beforehand.

Rishonim

Rambam (Hilchos Avodah Zarah 10:5): We finance poor Nochrim along with poor Yisre'elim, for Darchei Shalom.

Rambam (Hilchos Zechiyah 9:11): If one said "free my slave", we force his heirs to free him, for a slave is commanded about some Mitzvos.

Magid Mishneh (11): One who frees his slave transgresses an Aseh. Why do we do so? Meforshim gave many answers. The Rashba says that perhaps whenever a master commands to free a slave, we estimate that the slave did something nice for him, and the master is obligated to bestow to him in return. We do not establish people to transgress [this Aseh, and free without reason]. Therefore, it is like selling the slave to himself. The Torah forbids freeing a slave without [having received] a benefit, merely due to his desire. One knows why he frees!

Rambam (12): If one said 'make my Shifchah Plonis happy', we make her happy. She does only tasks she desires among all known tasks of slaves in that region.

Tosfos (Avodah Zarah 20a DH Rebbi): According to R. Yehudah, why do we need "v'Lo Sechanem" to forbid a gift to a Nochri? We can learn from Nevelah! I answer that v'Lo Sechanem forbids this through a Lav. The verse of Nevelah teaches an Aseh. Alternatively, it teaches that giving to a Ger is a real gift, and not for money. The Rivam asked that here R. Yehudah forbids giving a gift to a Nochri, but in Pesachim we establish the Mishnah of sending a thigh to a Nochri like R. Yehudah! [My] Rebbi answered that a Tosefta says that here R. Yehudah permits for a Nochri that he knows, for this is like selling to him.

Note: One could have answered that the Mishnah holds that the Gid has taste, like R. Yehudah, but holds like R. Meir regarding gifts to a Nochri. Tosfos' answer is better.

Tosfos (ibid.): In Eruvin, R. Gamliel told Ilai to give a gift to a Nochri, even though he did not know him. There is different, for he accompanied them on the road.

Note: Presumably, Tosfos did not answer that Mavgai was a Ger Toshav, for the Gemara calls him a Nochri.

Question: Does the opinion that forbids give a gift to a Nochri argue with the Mishnah that teaches that we finance poor Nochrim with poor Yisre'elim due to Darchei Shalom?

Answer (Tosfos): Darchei Shalom is not called a free gift.

Question: Does the opinion that permits give a gift to a Nochri argue with the Beraisa (Avodah Zarah 26b) that teaches that we push Nochrim into a pit [to die], and we do not raise them?

Answer (Tosfos): The verse discusses giving a gift that will not keep him alive. Even without the gift, he would live.

Chidushei ha'Ran (Gitin 38b DH Mitzvah): If one frees a slave for the sake of a Mitzvah, it is as if he pays his own value. This is not a free gift.

Poskim

Shulchan Aruch (YD 151:12): We finance poor Nochrim for Darchei Shalom.

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

Shach (2): 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 Mechaber (151:12) rules like the Ran.

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.

Beis Yosef (DH Asur): The Halachah follows R. Yehudah [against R. Meir - Eruvin 46b].

Beis Yosef (DH u'Mah): The Tur forbids giving a gift to one who serves idolatry. He does not come to exclude Yishmaelim, rather, a Ger Toshav who accepted the seven Mitzvos of Bnei No'ach. We are commanded to sustain him. All other Nochrim have the same law.

SMA (2): If a Ger Toshav does not have his own, it is a Mitzvah to sustain him. If he has, in any case one may sustain him. If a Nochri did not accept the seven Mitzvos of Bnei No'ach, even if he does not serve idolatry, one may sell to him, but one may not give to him, unless one will benefit from him, for this is like a sale. Similarly, one may give to him if he knows him, or if Darchei Shalom applies.

Be'er ha'Golah (3): Likewise, it is permitted if he accompanies them on the road, like the case in Eruvin.

Shulchan Aruch (256:4): If one said 'make my Shifchah Plonis happy', we make her happy. She does only tasks she desires among all known tasks of slaves in that region. (Some say that if she wants, we force them to free her.) See YD 267:77.

Beis Yosef (DH u'Mah she'Chasav Asu): It is clear from the Yerushalmi, Tosefta and Bavli that if he explicitly commanded to free her, the heirs must free her.

Beis Yosef (DH u'Mah she'Chasav she'Eved): The Tur [and Rambam] say that a slave is commanded in Mitzvos to explain why we give his body to him for a gift, for he is not a total Yisrael. Since he is commanded some Mitzvos, it is permitted. The Isur to give a gift is only to a total Nochri.

SMA (8): We do not heed one who says to do an Isur with his property. The master has Chezkas Kashrus. We assume that someone paid the slave's value to free him. Then, he must free him. This is not "for naught." The one who gave money does not transgress, for a slave is commanded some Mitzvos. This is unlike a gift to a Nochri. The Ran (Kesuvos 44a DH Shuda), and Rambam say so.

Prishah (5 DH she'Eved): The master does not transgress, since he repays a benefit that the slave did. However, one need not repay his own slave for a benefit. If so, the question returns! This is why the [Rambam and] Tur say that he is obligated in some Mitzvos. If one commanded to give to a Nochri, why don't we say that surely he received a benefit from him? It is difficult to say that since he did not benefit the heirs, they may not give to him, or that people are less aware of the Isur to give a gift to a Nochri than the Isur to free slaves. The Ran [who assumes that he received redemption money] does not need the reason that a slave is commanded some Mitzvos.

Note: If we assume that the master already received redemption money, we force the heirs to "free" the slave, i.e. merely to publicize that he is free.