What did they learn in the Yeshiva of Shem and Ever?
The Gemara in Sanhedrin 59a tells us that a גוי who learns Torah is חייב מיתה. If so what were they allowed to learn in Shem and Ever's yeshiva?
The Rambam quotes this halacha in Hilchos Melachim Perek 10. The Chasam Sofer points out that the Rambam in the other halachos writes בן נח, by Torah he writes גוי. The Chasam Sofer claims that the Rambam holds that the issur to learn torah only applies to an עובד עבודה זרה, however a בן נוח is allowed to learn torah. If so, this answers the question on Shem and Ever's yeshiva they were not עובד עבודה זרה and were therefore were allowed to learn Torah.
The פשטות is not like the Chasam Sofer and the issur would apply to all non-Jews. However, they are still allowed to learn the ז' מצות בני נח and anything related to them. Therefore we need to say that they learned the ז' מצות בני נח in Shem and Ever's yeshiva and not all of Torah.
The Gemara in Chagiga 13a says that אין מוסרים תורה to a גוי based on the pasuk that we say in davening every day ומשפטים בל ידעום. Tosafos there asks why do we need this pasuk, since a גוי is not allowed to learn torah, I am prohibited from teaching him so what is this pasuk מחדש, see Tosafos's answer. The Maharsha answers that this pasuk teaches us that you can't even teach them lomdus in the ז' מצות בני נח, from the gemara in Sanhedrin I would have thought that was mutar, comes the pasuk here to prohibit it. If so, again, what did they do in Shem and Ever's yeshiva? They were not even allowed to learn the reasons of the ז' מצות בני נח and any lomdus?
The answer would seem to be as follows. The source for the issur for a גוי to learn Torah is based on the pasuk תורה צוה לנו משה מורשה קהילת יעקב, the gemara in Sanhedrin says that either it means it is our inheritance and for a גוי to learn it is stealing, or it means מאורסה, engaged, that the Torah is like our bride. In either case the issur only came into effect after Matan Torah, before matan Torah the Torah did not belong to the Jewish people and was not married to the Jewish people. Therefore, the whole issur for a גוי to learn Torah only started after Matan Torah and consequently Shem and Ever and their yeshiva were allowed to learn all of Torah.
This issur is very relevant nowadays. How can I write this on my blog, after all, a גוי can come and read this and learn Torah? R' Moshe was asked this same question about shiurim on the radio and he answered that since you are teaching Torah to Jews you have no chiyuv to stop just because a גוי can listen in. The same applies to blogs. However, in a one on one situation the issur definately applies. For example, at work, if a גוי starts asking you all kinds of questions about Judaism it is not so simple that you can just answer him. There is a problem of teaching torah to a גוי. The same applies to e-mails from a גוי, you have to be very careful how you answer.