Are there Rabbinic prohibitions on non-Jews in the context of the 7 Noachide laws? e.g., would they have gezeirot like yichud or negia in order to prevent ariyot?
Mishneh Lamelech (on Rambam, Hil. Melachim 10:7, end of the first paragraph) states that "regarding Noachides, we never find anywhere that [the Rabbis] enacted preventative measures (seyagim) for them." So apparently not.
On the other hand, it would seem from the sources that they may, and perhaps should, enact their own precautionary measures. We are told that "since the world was punished with the Flood [caused, among other things, by rampant sexual immorality], the nations of the world took the initiative to fence themselves in regarding sexual matters." Lavan's shepherds criticized Yaakov for his apparent breach of this norm, in kissing Rachel in public (Bereishis Rabbah 70:12) - even though this is not technically prohibited under the Noachide laws.
The Lechem Mishna to the Rambam Hilchos Melachim 10:9 says that the fact that a non-Jew is not allowed to keep Shabbos or learn Torah is, in fact, a Rabbinic prohibition.
So according to that, there are in fact Rabbinic enactments that apply to non-Jews, but perhaps it is only, like those two, where specified.
The Rambam in Hilchot Nachalot 6:10 says "ואין הגוי מחוייב לעמוד בתקנת חכמים, a gentile is not obligated to keep rabbinic enactments." Likewise, the Mishneh Lamelekh (Melakhim 10:6), Ketzot HaChoshen (66:32), Chatam Sofer (Shu"t 6:25, Choshen Mishpat 66), and Shem Aryeh (Orach Chaim 1:11) explain that rabbinic enactments to not apply to gentiles.
However, a number of acharonim hold that Noahides can be obligated in mitzvot derabbanan. See for example R. Elchanan Wasserman, Kuntres Divrei Sofrim, 1:21-22. He gives the example of "beit din shel Shem" which enacted prohibitions before matan Torah. But obviously, bnei Noach do not automatically have all the gezeirot made for Jews, even for those mitzvot which apply to them. R. Shlomo Zalman Auerbach (letter printed in the beginning of Birkat Avot) offers the same approach as R. Wasserman. This position is also recorded in Shemirat Shabbat Kehilchata (1st ed., Ch. 32, n. 4). These sources are taken from Sefer Birkat Avot.
The Rema (in his Tshuvot, #10) writes that non-Jews must abide by the Jewish rules of Choshen Mishpat - civil law (and not their own laws).
Thus we do see a major area of law where the entire rabbinic structure of law is applied to non-Jews, and not just the Torah-level laws.