Is Al-Alusi’s statement that the veil over the khimar is part of the outer garments, the wearing of which does not lead to the exposure of 'awrah, or Al-Jassas’s statement that it is permissible for an old woman to uncover her face and hands because she is not desired, considered clear proof of the obligation for a Muslim woman to cover her face?

The covering of the face and hands is obligatory without dispute when there is a fear of fitna (temptation/strife). When there is no such fear, the Malikis and Hanafis do not consider it obligatory, whereas the Shafi'is and Hanbalis do. The aforementioned verse does not explicitly indicate the obligation of covering the face and hands. Rather, it is inferred by indication that the verse's permission for elderly women to lay aside their outer garments implies that young women are commanded to observe hijab (definition) and cover their faces. This meaning has been supported by evidence, yet the verse does not explicitly state it. You should act according to the opinion you incline towards, as it is more cautious for your religion, based on the saying of the Prophet, peace be upon him: "Leave that which makes you doubt for that which does not make you doubt," and his saying: "Righteousness is that with which the soul feels at ease and the heart feels tranquil, and sin is that which the soul does not feel at ease with and the heart does not feel tranquil with, even if the jurists give you a fatwa (definition) (religious ruling)."