Is it permissible for a woman suffering from a respiratory illness to uncover her face due to a feeling of distress caused by the face covering, and how sound are the hadiths that do not oppose uncovering the face and hands?

The basic principle is that it is obligatory for a woman to cover her 'awrah from non-mahrams, except in cases of necessity or dire need. If a woman is harmed by covering her face, it is permissible for her to uncover it due to necessity.

As for the hadith of Asma bint Abi Bakr: "O Asma, when a woman reaches menstruation, it is not proper that anything be seen of her except this and this," and he pointed to his face and hands, it does not establish a proof due to the presence of critical defects in it, including: discontinuity in its chain of transmission (sanad), the weakness of one of its narrators, who is Sa'id ibn Bashir, and the tadlis (deceptive narration) of Qatadah and Al-Walid ibn Muslim.