Obviously a non-Jew cannot keep Shabbos but what if, for example, they wanted to keep kosher and say brachos on food? Are they rewarded?
It would appear they are, although not to the same extent.
In the Kuzari (1:27) it is written:
"...non-Jews who wish to adhere to the Torah will share in the rewards like us, though not to the same degree."
The Gemarah in Kiddushin 31a says:
וְאָמַר רַבִּי חֲנִינָא: וּמָה מִי שֶׁאֵינוֹ מְצֻוֶּוה וְעוֹשֶׂה – כָּךְ, מְצֻוֶּוה וְעוֹשֶׂה – עַל אַחַת כַּמָּה וְכַמָּה. דְּאָמַר רַבִּי חֲנִינָא: גָּדוֹל מְצֻוֶּוה וְעוֹשֶׂה מִמִּי שֶׁאֵינוֹ מְצֻוֶּוה וְעוֹשֶׂה. And Rabbi Ḥanina says: And if this is related about one who is not commanded by the Torah to honor his father, as Dama was a gentile, and nevertheless when he performs the mitzva he is given this great reward, all the more so is one rewarded who is commanded to fulfill a mitzva and performs it. As Rabbi Ḥanina says: Greater is one who is commanded to do a mitzva and performs it than one who is not commanded to do a mitzva and performs it.
I think I remember reading somewhere that the reason they are rewarded less is because being commanded to do the mitzvos shows you truly believe in Hashem and want to follow His commandments, while a non-Jew may just be doing it as happenstance. If someone can clarify that would be great, because what if the non-Jew fully believes in Hashem and wants to serve him?
a noahide is allowed to follow the torah, considering he doesnt change the correct way neither creates a new religion. its very clear for me when readng rambam:
9 A gentile who studies the Torah is obligated to die. They should only be involved in the study of their seven mitzvot.
Similarly, a gentile who rests, even on a weekday, observing that day as a Sabbath, is obligated to die. Needless to say, he is obligated for that punishment if he creates a festival for himself.
The general principle governing these matters is: They are not to be allowed to originate a new religion or create mitzvot for themselves based on their own decisions. They may either become righteous converts and accept all the mitzvot or retain their statutes without adding or detracting from them.
If a gentile studies the Torah, makes a Sabbath, or creates a religious practice, a Jewish court should beat him, punish him, and inform him that he is obligated to die. However, he is not to be executed.
10 We should not prevent a Noachide who desires to perform one of the Torah's mitzvot in order to receive reward from doing so, provided he performs it as required. If he brings an animal to be sacrificed as a burnt offering, we should receive it.
No, gentiles earn no reward for observing commandments other than the seven Noahides laws. The Rambam writes:
[Gentiles] may become true converts [to Judaism] by accepting all the commandments or they must observe their own (seven Noahide) laws only, and not add or detract from them. [Mishneh Torah, Kings and Wars 10:9]