What is the ruling on the prayers of one who forgot to convey water to a small, dangling piece of skin on a toe during ablution, and is this considered a pardoned error and forgetfulness?

Water must reach beneath the drooping skin in wudu', because it has become part of the obligatory area. The proof for this is the statement of Al-Bahuti Al-Hanbali in "Kashshaf Al-Qina'": "Washing what is beneath it."

As for the issue that an interposition, if it is from the body, does not affect the validity of wudu', this applies when it is attached to the body, not separate from it.

The majority of scholars obligate making up prayers in which purification was not complete.

As for forgiveness for error and forgetfulness, it removes the sin from the doer, but it does not remove the ruling associated with it. So, whoever forgot wudu' and prayed, must repeat the prayer if it becomes clear that he prayed while in a state of impurity.

Error and forgetfulness make what exists as if it does not exist, but they do not bring into existence what does not exist. So, if one forgot rukūʿ (bowing), he must perform it.