Gemara

(Rava): (Mid'Oraisa, a Nochri can be Ma'arich, and Hekdesh uses his money.) Ezra decreed not to take their money for the Mikdash, lest Yisraelim slacken from contributing for it - "va'Yehi Am ha'Aretz Merapim Yedei Am Yehudah u'Mevahalim Osam Livnos."

Contradiction (Beraisa #2): We do not accept from him.

Resolution (Rav Ila): At first, we do not accept. In the end, we accept.

Sotah 21a (Ula) "Boz Yavuzu Lo (they will scorn him)" does not refer to Shimon, the brother of Azaryah. (He was called so, for his brother supported him.)

Bava Basra 9b - Question: Because one is "Rodef Tzedakah v'Chesed, he will (need and) find... Tzedakah"?!

Answer #1 (R. Yitzchak): Rather, anyone who pursues to do Tzedakah, Hash-m will enable him to give Tzedakah.

Answer #2 (Rav Nachman bar Yitzchak): Hash-m will present to him fitting recipients of Tzedakah, so he will get reward;

(Rabah): "Va'Yihyu Muchshalim Lefanecha" - Yirmeyah asked that even when (the people who wanted to kill him) try to do Tzedakah, Hash-m should present to them unworthy recipients, so they will get no reward.

Chulin 5a (Beraisa): "From you" teaches that we distinguish only among you (Yisraelim), but not among other nations. (Any Nochri may volunteer an Olah.)

"From an animal" includes people who resemble animals. This is the source that sinners of Yisrael may bring Korbanos, so that they will repent.

We do not accept Korbanos from a Mumar (wanton sinner), one who is Menasech (offers wine libations to idolatry), or one who publicly desecrates Shabbos.

Rishonim

Rashi (Zevachim 2a DH Shimon): Azaryah stipulated with Shimon that he will supply Shimon's needs, and receive a share in the reward for his Torah.

Hagahos Ashri (Bava Basra 1:36, citing Mahari'ach): Why do we accept Nedarim and Nedavos from Nochrim, but not Tzedakah? My Rebbi, R. Avraham, explained that Nedarim and Nedavos are not for atonement.

Poskim

Shulchan Aruch (YD 246:1): One who cannot learn, because he does not know how to learn at all, or due to distractions, should support others who learn.

Rema: It is considered as if he himself learned. Levi can stipulate with David that David will learn and Levi will supply his income and share the reward.

Shach (2): They share the reward, and also the money that Levi earns.

Maharam Alashkar (101, cited by R. Akiva Eiger): Rav Hai Gaon said that it is folly to think that one can sell the reward for fasts or Mitzvos that he did.

Minchas Yitzchak (7:87): The Poskim mention a partnership between Yisachar and Zevulun, but Chazal did not. The Medrash Rabah (Vayechi 99) says only that Zevulun engaged in business and fed Yisachar, therefore Zevulun was mentioned first (in the Berachah). Hash-m rewarded Zevulun, even though they never made a partnership. The source for a partnership is Sotah 21a. The Medrash mentions Yisachar and Zevulun together with Shimon and his brother Azaryah, therefore the Poskim discuss a partnership also regarding Yisachar and Zevulun. R. Yerucham (2:3) holds that they share the reward only if they stipulated from the beginning. However, this is unlike Chazal and the Rema. The Gra brings that the Rema's primary source is the Gemara in Sotah, and not R. Yerucham. Maharam Alashkar (101) brings that Rav Hai Gaon holds that such an agreement does not work. Even though the Halachah does not follow Rav Hai Gaon, if he held that Yisachar and Zevulun stipulated, he would not say that it does not help. I later found that the Medrash Rabah in Nasa (13:16) says that Yisachar and Zevulun stipulated.

Minchas Yitzchak (ibid., DH Emnam): The Midrash Rabah in Vayechi mentions that Yisachar helped work a little (to carry the merchandise on donkeys. I.e. such a partnership is valid even if Yisachar also does some work.)

Minchas Yitzchak (DH Hinei): If one supports many, surely some of them learn Lishmah. If one supports only one Chacham, perhaps he learns Lo Lishmah. R. Yitzchak and Rav Nachman bar Yitzchak argue about whether one gets reward for giving Tzedakah to unworthy people. If one totally supports one Chacham, he alone enables him to learn day and night. If many support together, this depends on the law of two who did a Melachah together. (Tana'im argue about this - Shabbos 93a). If Reuven sees that Shimon is not learning properly, surely he may cease to support him. If not, perhaps he cannot cease even if Shimon agrees, for this is like a vow. Perhaps this is why the Chazon Ish made a text of a contract only for a year (which can be renewed). L'Chatchilah, they should stipulate exactly what support will be given. If they merely stipulated 'all his needs', the way people speak at that time and place determines what this is, and whether lavish Seudos that people make for a wedding or Bris Milah are included.

Igros Moshe (YD 4:37 DH Aval Nir'eh): one cannot stipulate about the learning that everyone must know for himself. This includes learning Gemara, Rashi and Tosfos. Also Zevulun learned this! Rather, the partnership is for learning the entire Torah and going into depth. Most people after the generation of the Midbar cannot do this due to toil of income. A Bochur supported by his father should not enter into such a partnership, for he has no need for it.

Igros Moshe (18): Surely Zevulun must fix times for Torah, and learn when he is free. He need not learn all of Shulchan Aruch in order to know all relevant Halachos. Many Chachamim who learn the entire day do not know this! They rely on (knowing) what applies constantly, e.g. laws of Tefilah and Berachos, from the way they were raised. They know what a slaughtered bird should look like, and any deviation about which one must ask. All know the basic laws of theft, interest and swindling, Zenus, Nidah... They ask questions to a Rav. The partnership exempts from the obligation to know the entire Torah, including Kodshim and Taharos. Most cannot achieve this, unless they learn constantly their entire lives.

Shulchan Aruch (254:2): If a Nochri officer gave money for Tzedakah, we do not return it to him, lest this anger the kingdom. Rather, we accept it, and covertly give it to poor Nochrim.

Rema: Some say that we do what the officer commanded. This refers to money. If they donated something to the Beis ha'Keneses, we accept it. However, we do not accept from a Mumar.

Shach (5): The Mabit (1:214) says that we accept Hekdesh (Tzedakah) from Mumarim for Aniyim or a Beis ha'Keneses.

Minchas Yitzchak (6:100 DH v'Hinei): The Gemara says that we accept Korbanos from a Nochri, but not from a Yisrael Mumar or one who is Mechalel Shabbos in public. We do not we accept Tzedakah from a Nochri. Seemingly, all the more so one may not take from one who is Mechalel Shabbos in public. However, the Mabit (1:214) permits. Even though he sinned, he is still a Yisrael. Perhaps the merit of Tzedakah will help him to repent! He is worse than a Nochri only regarding Korbanos, for a verse excludes him.

Minchas Yitzchak: Maharam Shik (OC 81) says that the Gemara and Rambam (Hilchos Ma'aseh ha'Korbanos 3:4) permit taking Korbanos from a Mumar. He similarly permits to take for a Beis ha'Keneses or the Beis ha'Mikdash, as long as the sinner believes in Hash-m and His Torah. One who does not accept from them blocks their Teshuvah. This is astounding. The Gemara and Rambam explicitly forbid taking Korbanos from a Mumar! In any case, he gives a reason to permit accepting Tzedakah from a Mumar. We can add the opinion of Acharonim that nowadays, those who desecrate Shabbos are like Tinok she'Nishba (a baby captured by Nochrim; he cannot be blamed for not observing Mitzvos). Some discourage this, and especially to request from them, for the giver can influence the receiver.

Minchas Yitzchak (DH Emnam): If the supporter does not observe Torah and Mitzvos, surely he gets some reward for supporting Torah, but it is not clear whether one may make a partnership with him. Regarding a partnership, we should not discourage them from giving Tzedakah and supporting Torah. However, it is disgraceful if the Chacham's Torah comes from such a person. Maharam Shik permits taking from a Mumar for a Beis ha'Keneses, unless the donor's name will be on it. Here, the donor's name is on the Chacham's Torah! However, perhaps here is different. These are matters above our understanding. It is hard to add to what Chazal said.

Igros Moshe (ibid., 17): The supporter receives reward like the one who learned only they stipulated. The stipulation does not apply to one who does not believe (that Hash-m commanded about the Mitzvos). If he believes, but he sins because he cannot stand up to his desire to increase wealth, he would not give half his earnings. It would be better that he not desecrate Shabbos, even without receiving reward for Torah. He thinks that the stipulation allows him to desecrate Shabbos, or at least it will atone for it. One must tell him that all that he gives for Tzedakah and learning will not atone for him until he ceases to desecrate Shabbos and repents for the past. One who makes a partnership with him benefits from Chilul Shabbos. Surely one may not do so. Such a stipulation is void. Surely the giver gets some reward for it; Hash-m will decide what it is.

Igros Moshe (ibid., 20): The agreement must be equal. They share the money earned, and the reward of Torah both in this world and in Olam ha'Ba. The giver cannot give less than half his income, for this would disgrace the importance of Torah. One cannot stipulate to give less than half the reward, lest this cause people to slacken from doing like Zevulun. Yisachar must be able to learn comfortably, with confidence that Zevulun will be able to supply his needs. The agreement must be for a period long enough for Yisachar to become Chacham in Torah. Kesuvos 62b connotes that this is at least three years. However, there is no explicit source for this. Perhaps even one year is enough. Zevulun must appreciate the importance of Torah.

Halichos v'Hanhagos (p.71): R. Y.S. Elyashiv, Shlita says that the agreement works only if otherwise, Yisachar would be working, but not if in any case he would be learning.