What is the ruling on feathers fallen from live or dead birds, such as pigeons and crows? And is it considered ritually impure if one prays with them or in a place where they are present, intentionally?

The feathers that fall from an animal whose meat is permissible to eat are pure according to the majority of scholars, whether they fall during its lifetime or after its death. As for feathers that fall from an animal whose meat is not permissible to eat, they are pure according to the Hanafis and Malikis, in contrast to the Shafi'is and Hanbalis who consider them impure if they are from a carcass other than that of a human. If you pray in a place where impure feathers have fallen, and the impurity is dry, your prayer is valid. However, if you pray with impure feathers, and you are aware and intentional, your prayer is invalid. But if you are ignorant or forgetful, you are not required to repeat it.