In Gittin 33a, Kesuvos 3a we learn that Rabbanan have the power to uproot a kiddushin because:
כל דמקדש אדעתא דרבנן מקדש ואפקעינהו רבנן לקידושין מיניה
When a man betroths a woman, he does so under the conditions laid down by the Rabbis, and in this case the Rabbis annul his betrothal.
My question revolves on how to fully understand this principle:
1) Source for it? Is it d'oraisa or d'rabanan?
2) Why does this principle exist by kiddushin/ geirushin specifically?
3) What is the rationale for it existing? We don't extend this principle in other areas like "when a person makes a sale, he does so under the conditions laid down by the Rabbis"