I have tried to understand this in other ways, but it seems that the Talmud is saying it is okay for a jew to steal from a non-jew.
"i. If a Nochri takes from a Nochri or from a Yisrael, it is forbidden; a Yisrael is permitted to take from a Nochri."
And then, that it's okay for a jew to kill a non-jew:
"(i) Question: Whenever he is liable, the Tana says so!
1. (Beginning of the Beraisa): If a Nochri kills a Nochri or a Yisrael, he is liable;
i. If a Yisrael kills a Nochri, he is exempt.
(j) Answer: There, there was no other way to teach!"
I cannot accept that explenation. I believe I am not seeing something here, and would appreciate it if you could clear this for me.
N.B., Los Angeles, CA
As we have written elsewhere, these statements in no way imply what you are inferring from them, as is evident from all of the sources and from the context of the statements that you quote.
To address your specific questions:
The first statement that you quote in Sanhedrin 57a is said with regard to a non-Jew (or, more specifically, a "Kuttite" as the Talmud says), who *does not follow the Noahide Laws*. As the Me'iri explains clearly, a non-Jew who does not follow the law against stealing forfeits the right to have his own property protected by that law! In contrast, a non-Jew who does not flout the prohibition against stealing is protected by that law, and it is absolutely forbidden to steal from him. This is also clearly stated by the Code of Jewish Law (Choshen Mishpat 358:2): "One who steals even as little as a Perutah's worth *transgresses the Biblical prohibition* against stealing and must repay, whether one steals from a Jew or whether one steals from a non-Jew, and whether one steals from a minor or from an adult."
This also explains your second question that "it's okay for a jew to kill a non-jew": First, the statement that you quote does not say that it is "okay." It obviously is forbidden to kill anyone, as is clear from the Talmud and from the Halachic sources. The word that the Talmud uses there is that one is "exempt." This means that the death penalty is not meted out for such an act. Again, this applies only to killing a non-Jew who, himself, does *not* follow the prohibition against killing. His own decision to act in such a way and to kill other people forfeits his own right to be protected by the law, to some degree (such that one who kills him is not killed as a punishment, although it remains forbidden for a Jew, or non-Jew, to kill anyone, even a person who does not follow the law against killing).
Please let me know if we have addressed your questions adequately.