Gemara

(Reish Lakish): If a Nochri did not work for an entire day, he is Chayav Misah - "v'Yom v'Laylah Lo Yishbosu";

A Nochri is Chayav Misah for transgressing any of his Mitzvos.

Yevamos 47b (Beraisa): If a Yefas To'ar (a beautiful Nochris taken in war) accepts to convert; she immerses and she is permitted to him immediately;

R. Shimon ben Elazar says, even if she did not accept, he may immerse her to become a slave, and immerse her again to free (convert) her.

(Rav Papa): Chachamim argue only about a Yefas To'ar. A slave is already commanded in Mitzvos, so they would agree that one may immerse him Bal Korcho (against his will!)

48b (Beraisa - R. Yishmael): One may keep slaves who refuse to be circumcised - "the son of your slave will rest."

R. Akiva: One may not keep them. The verse discusses one who bought a slave just before Shabbos, and did not have time to circumcise him.

Question: All agree that the verse discusses an Arel (uncircumcised) slave. How do they know this?

Answer (Beraisa): "Your slave will rest like yourself" teaches about circumcised slaves, so "your slave's son will rest" must discuss an Arel slave.

"The Ger in your gates" refers to a convert, so "(your slave's son will rest) veha'Ger" must refer to a Ger Toshav (one who accepted the seven Mitzvos of Benei Noach).

(R. Yehoshua ben Levi): If a slave bought from a Nochri refuses to circumcise, one may keep him for 12 months. After that, he sells him to a Nochri.

Rav Papa: This can be even like R. Akiva. We distinguish between Poska (he fixed the matter) and Lo Poska (this will be explained).

(Ravin): One may keep an Arel slave only if he bought him intending not to circumcise him.

Rav Papa: This can be even like R. Akiva. R. Akiva forbids when there was no stipulation not to circumcise him. If he stipulated, it is permitted.

Krisos 9a (Beraisa - R. Shimon): A Ger Toshav, Nochri or slave of a Yisrael may do Melachah for himself on Shabbos.

(Rav Ada): The Halachah follows R. Shimon.

Rishonim

Rif (Yevamos 16b): Rav Papa concluded that Tevilah is needed to become a slave or become free, but a slave bought from a Yisrael need not accept the Mitzvos, for he already accepted beforehand.

Rambam (Hilchos Isurei Bi'ah 14:9): If one buys a slave from Nochrim, we say 'do you want to be a slave of Yisrael and be Kosher, or not?' If he does not want, we wait 12 months, then sell him to Nochrim. One may not keep him longer. If he stipulated from the beginning that he will not circumcise or immerse, one may keep him for a Ger Toshav, but only when Yovel applies.

Rambam (Hilchos Avodah Zarah 10:6): When Yisrael has the upper hand, we may not leave an idolater among us, even to dwell temporarily or pass through on business, until he accepts the seven Mitzvos of Benei Noach.

Magid Mishneh (Hilchos Shabbos 20:14): The Rambam (in the Halachos above) connotes that one may not keep an Arel slave who serves idolatry. He holds that Yevamos discusses keeping an Eved Arel. The Ramban agrees. The Rashba says that even if he did not accept any Mitzvos, a Yisrael may not tell him to do Melachah. He would forbid even needs of Choleh she'Ein Bo Sakanah (a sick person who is not in danger) or to bury a Mes on the first day of Yom Tov. The Rambam's opinion is primary.

Rosh (Yevamos 4:38): R. Akiva could agree that if one bought a slave from a Nochri and the slave refuses to be circumcised, one may keep him for 12 months, i.e. if he agreed to be circumcised, then retracted. Rashi explains that Lo Poska is when he never agreed to circumcise and cease being a Nochri. If he agreed to convert (partially, to become an Eved Kena'ani) and retracted, we wait (12 months), for perhaps he will agree again. Alternatively, we may not keep him Stam when no deadline was fixed. When he said 'I will keep you only 12 months. If you do not circumcise by then, I will sell you', it is permitted, for he is like a mere hired hand. Rav Hai Gaon forbids keeping him when he did not explicitly say that he will not circumcise; rather, he agreed, but keeps delaying. We do not delay Mitzvos. If he said that he will not circumcise, there is no Mitzvah to circumcise him Bal Korcho, so we wait 12 months, for perhaps he will agree. I explain according to Rashi that one may immerse a slave Bal Korcho, without acceptance of Mitzvos. Why don't we do so here? It is an enactment not to forcibly immerse him, lest the slave cause his master to transgress Isur v'Heter, since he refuses to accept Mitzvos. It is not good to obligate him in Mitzvos if he does not want to observe them. We said that a slave is already commanded in Mitzvos, so all agree that one may immerse him Bal Korcho. Rashi says that he lived in the Yisrael's house many days and fulfilled Mitzvos. This connotes even if he did not accept when he immersed to become a slave. The Rif connotes that Tevilah for slavery requires consent and acceptance (of Mitzvos).

Poskim

Shulchan Aruch (OC 304:1): If a slave did not circumcise and immerse, but he accepted the seven Mitzvos, he is like a Ger Toshav. He may do Melachah for himself on Shabbos, but not for his master. No Yisrael may tell him to do Melachah on Shabbos for a Yisrael, even one who is not his master. If he did not accept any Mitzvah, rather, he is a full Nochri, his law is like one who accepted the seven Mitzvos. The Halachah is, we tell a Nochri to do needs of a Choleh she'Ein Bo Sakanah, and to bury a Mes on the first day of Yom Tov. One may not tell the slave of a Yisrael to do so, even if he serves idolatry. Since the Torah forbids his Melachah, we permit only for Piku'ach Nefesh.

Beis Yosef (DH ul'Inyan): The Rashba says so about one who did not accept Mitzvos (Magid Mishneh). The Ran, Nimukei Yosef, R. Yerucham, Semag, Sefer ha'Terumos, Mordechai and Tur agree.

Source (Gra 12): Krisos 9a permits a slave to do Melachah (only) for himself. It did not say that this refers to an Eved Toshav. Also, we need no verse for an Eved Toshav, for he is included in Ger (Toshav)!

Note: I do not understand the first proof. There it says that also a Nochri may do Melachah for himself, even though the Torah permits Amirah l'Nochri (telling him to do Melachah)!

Gra (13): The Isur Amirah l'Nochri (for a regular Nochri) is only mid'Rabanan, therefore we permit for a Choleh or for burial on Yom Tov.

Shulchan Aruch (ibid): Some disagree and permit. In any case, if he does his master's work, and it is clear that this is without his master's Da'as (will), it is permitted and one need not stop him (Rema - even if he accepted the seven Mitzvos). If he does for another Yisrael who is not his master, even if it is l'Da'as Yisrael, it is permitted, as long as a Yisrael does not benefit from it on Shabbos. Some say that as long as he did not accept the seven Mitzvos, since he is a full Nochri, his master is not commanded about him. According to this, he may tell him to do needs of a Choleh she'Ein Bo Sakanah, and for burial on Yom Tov.

Gra (19): The Rambam holds that Yevamos discusses one who he accepted the seven Mitzvos, for if not, we are commanded to kill him!

Mishnah Berurah (15): One should be stringent like the first opinion. Due to Lifnei Iver, one may not tell a Kara'ite (who does not accept Oral Torah) or apostate to do (even the latter's own) Melachah on Shabbos.

Shulchan Aruch (3): If a Yisrael hired a full Nochri, the Yisrael is not commanded about the Nochri's rest on Shabbos.

Gra (25): Mo'ed Katan 12a says that a Nochri hired for a week or month... may tend a Yisrael's flock on Shabbos.

Beis Yosef (DH veha'Ga'on): Mahari Avuhav says that since Yishmaeli slaves can accept Islam and free themselves, they are not like Arel slaves, rather, like hired Nochrim. We infer that one who hired a Nochri is not commanded about the Nochri's rest. The Mordechai (Shabbos 462) agrees.

Mishnah Berurah (25): The Acharonim (e.g. Taz 3) say that one should be stringent, for it is a Safek Isur Torah, especially where slaves cannot free themselves through accepting Islam.

Bi'ur Halachah: The Magen Avraham says that if a hired Nochri accepted the Mitzvos of an Eved Kena'ani, his master is not commanded that he rest, but he himself may not do Melachah, for he accepted all the Mitzvos of women. Surely this is no worse than accepting the seven Mitzvos, which makes one a Ger Toshav and Yisrael are commanded to sustain him. A Ger Toshav may not rest on Shabbos. This Nochri accepted more, so he may observe Shabbos. If one accepts all the Mitzvos except for one, we do not accept him (Bechoros 30b), i.e. to be a full convert, but he is a Ger Toshav.