Shalom and thank you for your manifold question. You ask many good questions, and I will try to bring them into the context of Jewish law as well as the spirit of the law. I would like to start with the spirit of the law a little and then move on to the letter. The Talmud (Brachot 8:1) says that “since the day the Temple was destroyed The Holy One Blessed be He has in His world only the four cubits of Halacha (in which to reside)”. What this means is that, lacking as we are, the special connection we had when G-d revealed himself to us through certain miracles in the Holy Temples, if we seek to connect with G-d, it can only be within the framework of Jewish law. Those miracles were a matter of reciprocity, for example, a Jew would offer a sacrifice, (certain kinds) and a G-dly fire would come and consume it. (First Temple). When we keep the Halacha, we do not unfortunately see G-dly fire responding to us, or in fact any other open manifestation of response from G-d. However, if we really want to connect to what we believe is good and true and part of G-d’s infinite wisdom, the only way is through keeping the mitzvot. G-d however, is not a mean man in the sky. On the one hand, we indeed cannot understand much of the Torah, because G-d is infinite and we are finite, intelligent as we may be. The Torah is G-d’s infinite wisdom. On the other hand, the more we learn, the more we can see that the Torah is designed for humans and ways can be found to reconcile apparent contradictions or difficulties, much of the time in any case. (We await the prophet Elijah for resolution of the remaining issues.)
In the Babylonian Talmud (Shabbat 68:B) a scenario is brought forth whereby a Jew who forgets that it is the Sabbath day and transgresses many prohibitions, and this occurs many times over, is only obligated to bring one sin offering, (when his mistakes become clear.) Under what kind of circumstance could such mistakes occur, and why such a seemingly light ‘penitence’? {Repentance requires acknowledgement of the sin, sincere regret and resolve to change one’s ways. Sacrifices are only a part of the process.) The reason is that it is likely that if such a situation occurs, it is because that Jew had been captured as a child and raised among non-Jews. History is replete with such occurrences, we have only to recall how many Jewish children were raised in convents, monasteries and homes of non-Jews during the bitter Holocaust years. Today, after the Holocaust of W.W.11, there is another kind of Holocaust, called assimilation. Many many Jews have been raised either among non-Jews, having little or no knowledge of their heritage, or even in a traditional upbringing but one where their parents/teachers/guardians were not able to fully convey the true messages of Judaism. Thus, many people nowadays fit into the category of ‘the captive child’. It could be that no-one is considered a true apostate in our day, since a true apostate must be well-versed in Torah, and choose to rebel. Even people who are fairly knowledgeable for THIS generation are not necessarily in that category. In fact the Rambam even includes Karaites in the category of ‘captive child – Tinokot shenishbu’. So it seems no one is going to run and remove the ladder when his fellow falls into a pit. G-d forbid. This concept of ‘captive child’ is explained in the Mishneh Torah of the Rambam, HIlchot mamrim ch. 3 Halacha 3.
Regarding a non-Jew studying Torah, it states in Vayikra 18 “a person – ‘adam’ – shall do them and live by them.” The Sages comment on this “it does not say Cohanim, Levyim, or Israelites, rather it says ‘adam”’ and a non-Jew who studies (the Seven Noahide Laws) is considered as a Cohen Gadol, a high priest. The six hundred and thirteen mitzvot however, were given to the Jewish people specifically as their heritage, so it is not to be shared with a non-Jew, especially in a situation where a Jew teaches him/her. What happens if you are a university lecturer, and there are non-Jews in your classes? If this is your job, you may teach them, especially if there are also Jews you are teaching in the class. It is more problematic to teach one-on-one, or answer questions privately, unless it is reasonable to expect that this will bring the non-Jew to true belief in G-d, which is part of what the non-Jew is commanded in any case.There is room for leniency also if the teaching will bring benefit to the Jewish people, or at least prevent hatred. (An example of this might be explaining how Jews are forbidden to consume blood in order to avert a blood libel.) There are sometimes situations where enemies of the Jewish people take interest in our laws and traditions in order to cause us harm, G-d forbid, and of course we do not wish to hand them a ‘sword’.
A non-Jew who is in the process of conversion is allowed, according to many opinions, to learn the entire Torah, because when the conversion process is finished, he/she will immediately be obligated in the performance of the mitzvot and therefore must know how to keep them.
Today a Jewish court cannot mete out a death penalty because it does not have the powers that the Sanhedrin had during the Temple period. We do not and cannot negate G-d forbid what is written in the Talmud (Gemarah,) but as I explained above the law itself has provisions for different situations and circumstances. There are the Thirteen Principles of Torah exegesis which are the tools that were handed down together with the Torah and they enable Torah scholars to arrive at the relevant conclusions to individual situations.