Is the area below the chin considered part of the face according to any of the four madhhabs, and does this entail that a woman is not obliged to cover it during prayer and is obliged to wash it during ablution?

The majority of scholars hold that it is not obligatory to wash the area under the chin during ablution. The Shafi'is, however, believe it is obligatory to wash the area under the chin along with the face to ensure that the entire face is covered by the washing, not because it is considered part of the face. As for covering it during prayer for a woman, it is obligatory.