Is it permissible for a woman to show her ears along with her face, based on the prophetic hadith that considers the ears to be part of the face?

The ears are not considered part of the face in the context of awrah (that which must be covered), and a woman must cover them. The ear is awrah. If a woman reaches puberty and does not cover her ears and head, her prayer will not be accepted. Jurists have unanimously agreed that a woman should cover her ears, both their outer and inner parts. This indicates that their ruling is the same as that of the head concerning wiping (in ablution), not the face.

Aisha's hadith (definition), "My face prostrated to the One who split its hearing and sight," does not explicitly state that the ears are part of the face. It has not been authentically reported that the Prophet (peace be upon him) washed his ears; rather, what is established is only wiping them. The most preponderant opinion is that the ears are part of the head, based on the Prophet's (peace be upon him) saying: "When he wipes his head, sins depart from his head until they depart from his ears."

This hadith is mentioned in the chapter of ablution and ritual washing, not in the chapter of covering the awrah. The preponderant opinion is that covering the entire face is obligatory.