Is it possible to rely on Ibn al-Mubarak’s principle, “If one doubts hadath (ritual impurity), then wudu’ is not obligatory upon him until he attains a certainty he can swear by,” to get rid of the many doubts and whispers concerning purity?

The fundamental principle is that what was, remains as it was. So long as you have ablution, you are in a state of purity until a nullifier is confirmed. Doubt concerning a nullifier is not taken into consideration by the majority of scholars. The proof for this is the Prophet's (peace be upon him) hadith: "He should not leave (his prayer) until he hears a sound or perceives a smell," meaning he is certain of the presence of one of them. This hadith is a great principle and rule, indicating that things are judged to remain in their original state until the contrary is certain, and an incidental doubt does not harm this. So, whoever is certain of purity and doubts about impurity is judged to remain in a state of purity, whether the doubt occurs during prayer or outside of it.