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 expiation for perjury?
One who commits perjury should repent, seek Allah`s forgiveness and offer an expiation which is: feeding ten indigent persons, or clothing them, or giving a slave his freedom, but if that is beyond his means then, he should fast for three days. Allah, The Almighty, Says in this regard (What means): "Allah will not call you to account for what is futile in your oaths, but He will call you to account for your deliberate oaths: for expiation, feed ten indigent persons, on a scale of the average for the food of your families; or clothe them; or give a slave his freedom. If that is beyond your means, fast for three days. That is the expiation for the oaths ye have sworn. But keep to your oaths. Thus doth Allah make clear to you His signs, that ye may be grateful." [Al-Ma`idah/89].
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.
Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.