Is it permissible to uncover the face without adornment, adopting the juristic opinion that permits it without sin? And is the statement, "O Lord, if You get me out of this predicament, I will wear the niqab," considered a vow to Allah during severe distress, and does not fulfilling it entail sin?

The preponderant opinion is that covering the face is obligatory. It is also more prudent for a woman and safer for her faith and honor. Regarding vowing to cover the face: if the intention is to commit to the obligation of covering, then it is a vow to an obligation, which, according to the majority of scholars, is not valid. However, if it is a vow for something recommended by شرعًا (based on the opinion that covering is not obligatory), then it is binding to fulfill it, and it is not permissible to be released from it except in case of inability.