Gemara

71b (Beraisa): If a Nochri (Tony) wanted to return his loan on Ribis to Levi, and Shimon said 'give to me the money, and I will pay you like you must pay to Levi', if Levi authorized him to do so, this is forbidden.

This is a stringency.

Version #1 - (Rav Ashi): A Nochri cannot be (or make) a Shali'ach only for Terumah, but for other matters, he can!

Rejection: That is wrong! A Nochri cannot be a Shali'ach for Terumah, for we learn from "Gam Atem" - just like you are Bnei Bris (bound by the covenant of circumcision, i.e. Yisrael or a slave), also your Sheluchim must be. We learn from Terumah that Sheluchim work in general!

Version #2 (Rav Ashi): (A Nochri cannot be a Yisrael's Shali'ach due to "Gam Atem" - your Sheluchim must be Bnei Bris, just like you. This is our source for Shlichus. We learn that only Atem (Yisrael) can have Sheluchim!

(Ravina): Granted, a Nochri cannot have a Shali'ach, but (some texts - mid'Rabanan), he has Zechiyah (a Yisrael can acquire for him).

We find that even though a minor cannot have a Shali'ach, he has Zechiyah (some texts - mid'Rabanan). The same applies to Nochrim!

Rejection: No. A minor (Yisrael) can be a Shali'ach when he matures, so he has Zechiyah even when he is a minor. A Nochri can never be a Shali'ach, so he does not have Zechiyah.

Avodah Zarah 71a (Beraisa): Reuven may not tell a Nochri 'go in my place to (pay) the king's officer' (to pay my debt with Yayin Nesech).

Kesuvos 11a (Rav Huna): If a minor wants to convert, we immerse him (in a Mikveh to convert him) on the volition of Beis Din.

This is because Zachin l'Adam she'Lo b'Fanav.

Rishonim

Rambam (Hilchos Shluchim 2:1): A Nochri cannot be a Shali'ach for anything. A Yisrael cannot be a Nochri's Shali'ach for anything. It says "you will take Terumah Gam Atem" - just like you are Bnei Bris, also your Sheluchim must be. The same applies to the entire Torah. Also, the Meshale'ach must be a Yisrael in the entire Torah.

Rosh (Gitin 1:17): (Chachamim enacted Ma'amad Sheloshtam, that if Reuven tells his Shomer (or borrower) to give the deposit (or loan) to Levi', if all are there, Levi acquires.) R. Tam says that this was enacted for Yisrael, but not for Nochrim. The Ri says that if the Shomer (or borrower) was a Nochri and the giver and receiver were Yisre'elim, it does not work, for Ma'amad Sheloshtam is no better than proper Zechiyah; a Nochri cannot be Zocheh. If the recipient was a Nochri and the giver and Shomer were Yisre'elim, as long as the giver agrees to give it, the recipient may do so, but the giver can retract, for there was no Kinyan. If the giver was a Nochri and the recipient and Shomer were Yisre'elim, the recipient acquired. If Chachamim uproot a Yisrael's money through Ma'amad Sheloshtam, all the more so they uproot a Nochri's.

Rosh (2:27): Bahag says that if a Nochri brought a Get and gave it to a Yisrael to give to the wife in front of Edei Mesirah (witnesses), l'Chatchilah she may not marry, for divorce does not apply to Nochrim. B'Di'eved it is Kosher, like R. Shimon (who say that Edei Mesirah empower a Get). This is astounding! If the Nochri appointed the Yisrael to give it, it is Pasul even b'Di'eved, for a Nochri cannot be a Shali'ach; also, divorce does not apply to him. If he delivered a document appointing the Yisrael to give it, it is Kosher, for he merely delivered it, like a monkey could. R. Tam often sent a Get or Kidushin in this way! The Yerushalmi says that (when the Nochri appoints the Yisrael) there is not even a scent of a Get (if her husband will die, she may marry a Kohen).

Rashi (Bava Metzia 71b DH Bishlomo): Mid'Rabanan, we are stringent to say that a Nochri can be a Yisrael's Shali'ach.

Hagahos Maimoniyos (Hilchos Malveh 5:6): R. Chananel says that mid'Rabanan, we are stringent to say that a Nochri is a Yisrael's Shali'ach (e.g. for Ribis). R. Tam says that he is not a Shali'ach even to be stringent.

Tosfos (Kidushin 3a DH v'Ishahm citing R. Tam): One can give Harsha'ah (power of attorney) to a Nochri, but the Nochri must do Chalipin himself, for the witnesses cannot be Zocheh for him.

Tur (CM 123:15): We say that Harsha'ah is Shlichus; this means only that the Shali'ach cannot keep the money for himself.

Terumas ha'Deshen (313): Rav Nachman (Bava Metzia 66b) says that if Reuven sold the fruits that will grow on his tree, he can retract even after they grow, but if the buyer ate them, he need not pay. The Rosh (5:32) says that R. Tam learns from here that if one sold a loan document through Mesirah (giving it over) alone, and the buyer collected the debt, the seller can no longer retract. Even though one acquires a document only through writing another document and Mesirah, since the buyer already consumed, we do not take from him. The same applies if Levi authorized David to collect Levi's debt from a Nochri. Levi can retract until David collects it. The Rosh holds like R. Tam only when the seller knew about the collection, for he pardons it. If not, the borrower still owes the seller, for he should not have paid one who did not properly acquire the debt.

Poskim

Shulchan Aruch (CM 126:22): Some say that Ma'amad Sheloshtam works with a Nochri Shomer or borrower. Some disagree.

Tur: The Rif holds that it works with a Nochri.

Rema: In any case, if the Nochri already gave it to the recipient, we do not remove it from him.

Rebuttal (Shach 94): This is not always true. However, here it is true, for even without Ma'amad Sheloshtam, since the giver authorized him to give and he did his Shlichus, it is as if the giver himself gave.

Question (Ketzos ha'Choshen 15): Why does it help here? A Nochri cannot be a Shali'ach! Surely, if one told a Nochri to give something to Ploni, Ploni does not acquire, for Ein Shlichus l'Nochri! If one made a Nochri a Shali'ach to sell his Chametz, it is invalid; he transgresses owning Chametz during Pesach, and it becomes forbidden! It is no better here because he told the recipient to take it. Since it was not in the giver's Reshus, it is like Davar she'Lo Ba l'Olam! The Terumas ha'Deshen holds that Tefisah (seizure) helps whenever the Kinyan did not work. If Reuven tells Shimon to give to a Nochri, this is Shlichus. If he tells a Nochri to give to Shimon, it works only due to Tefisah. Shimon may keep it, but the Nochri still owes Reuven. We learn from when Tony was about to pay Levi, and Shimon asked to borrow the money and pay the Ribis (Bava Metzia 71b). We are stringent to forbid when Levi authorizes this. If Tony no longer owes Levi, letter of the law it is forbidden!

Shulchan Aruch (188:1): A Nochri cannot be a Shali'ach for anything. A Yisrael cannot be a Nochri's Shali'ach for anything.

Beis Yosef (DH Ein): It is known that the Halachah follows the latter version. The Rambam rules like this.

Shulchan Aruch (243:14):.A Nochri cannot be Zocheh, for he can never be a Shali'ach. Just like a Yisrael cannot be a Nochri's Shali'ach, he cannot be Zocheh for a Nochri.

SMA (27): A Nochri cannot be Zocheh for another, since he cannot be a Shali'ach. Similar, a Yisrael cannot be Zocheh for a Nochri, since a Yisrael cannot be a Nochri's Shali'ach.

Beis Yosef (YD 169 DH v'Im, citing Sefer ha'Terumos): One cannot be Zocheh for a Nochri. Even a Nochri cannot be Zocheh for a Nochri.

Machaneh Efrayim (Shlichus 14): Rashi holds that we are stringent to say that a Nochri can be a Yisrael's Shali'ach. This is why one may not tell a Nochri 'pay my debt with your wine.' The Ramban explains that the Yisrael paid the Nochri, so he acquired the Yayin Nesech and benefits from it. R. Tam holds that a Nochri is not a Yisrael's Shali'ach at all, and a Yisrael does not acquire from a Nochri with money! (This is left difficult.)

Chavos Ya'ir (49): According to the opinion that we are stringent to say that a Nochri is a Yisrael's Shali'ach, letter of the law one may not tell a Nochri to tell another Nochri to do Melachah on Shabbos.

Shulchan Aruch (YD 268:7): If a minor orphan Nochri came to convert, Beis Din converts him, for Zachin l'Adam she'Lo b'Fanav.

Question: A Nochri has no Zechiyah even mid'Rabanan!

Answer #1 (Tosfos and Hagahos Ashri 1:23): One who converts has Zechiyah mid'Rabanan, for he will have Shelichus. Alternatively, he is like a Yisrael regarding this Zechiyah because it makes him a Yisrael.

Answer #2 (Tosfos Sanhedrin 68b DH Katan): This is unlike other Zechiyos. Beis Din does not acquire for him. The convert acquires himself. All Yisrael, including minors, converted at the time of Matan Torah.

Answer #3 (Ketzos ha'Choshen CM 243:7): Beis Din is different. (It can be Zocheh even when a person could not.)