In the Kiddushin the man says: הרי את מקודשת לי, בטבעת זו, כדת משה וישראל My question is why the formulation is "כדת משה וישראל"? Is the meaning something in the sense of: "According to the Torah of Moshe Rabbeinu and of the nation of Israel" (while the Torah of Moshe Rabbeinu and the Torah of Israel are actually the same Torah, and the Rabbinical mitzvot are part of the Torah, pertinent to our time/situation)? (Is part of the intention also to proclaim that "under any and all circumstances (taking into account possible misunderstandings of people) the Kiddushin is valid" ?) Thank you very much in advance

The first part of your explanation is correct, if I may just add that the legitimacy and power of the rabbinic mitzvot are dependent upon their being accepted by the “Nation of Israel”. On the other hand, the context in which the term is used (e.g. Gittin 33a; Bava Batra 48b) is davka to stress that the kiddushin is conditional, and the rabbis have the power (even though it is extremely rarely used) to retroactively revoke or invalidate Kiddushin when something (even at a later date) is not done in accordance with halacha and the wishes of the rabbis.