Is it permissible for a woman to pray in tight clothing that defines the 'awrah (parts of the body that must be covered), knowing that it is opaque and does not reveal what is beneath it? And why, if it is sufficient for covering the 'awrah during prayer, is it not sufficient in front of other women?

A woman's prayer in tight clothing is valid, but this does not mean it is permissible for her to go out in it in front of women or men. This is because what validates prayer does not necessarily correspond to what a woman may reveal in front of others. For example, a woman uncovers her face and hands in prayer, but it is not permissible for her to display them in front of non-mahram men. Similarly, a man is commanded to cover his shoulder in prayer, but it is permissible for him to uncover it outside of prayer. Ibn al-Qayyim and Ibn Taymiyyah clarified this by stating that the awrah for looking is different from the awrah for prayer. A woman is commanded to cover herself in prayer with what is called a "sitra," and outside of prayer, she wears modest clothing that does not reveal the size of her limbs.