How does the person praying perform the prostration (Sujud)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is an act of Sunnah for the person praying to descend for prostration (Sujud) by placing their knees first, then placing their hands on the ground, and then placing their nose and forehead simultaneously. It is obligatory that the toes of the feet be on the ground, directed towards the Qibla. And Allah the Exalted knows best.
Does passing wind from the anus affect ritual purity?
Ablution is nullified by the passing of wind from the anus, but washing the anus is not required as wind leaves no impurity.
What is the ruling on forgoing the sacrifice (uḍḥiyah) for one who is financially able to offer it?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
It is disliked (makrūh) for one for whom the uḍḥiyah (sacrifice) is recommended (Sunnah) to forgo offering it, on account of the scholarly disagreement regarding whether it is obligatory. And Allah, the Most High, knows best.
Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).