What is the ruling on performing istinja' after passing wind from the anus?
Ablution is invalidated by passing wind from the anus, even without a smell. Only ablution becomes obligatory from it. Istinja' is not obligatory nor recommended. And Allah the Almighty knows best.
Is it permissible for women to attend Tarawih prayer in the mosque?
Yes, it is permissible for women to attend Tarawih prayer in the mosque, provided they observe modesty, proper covering, and avoid mixing with men.
The Prophet ﷺ said: "Do not prevent the female servants of Allah from the mosques of Allah." [Bukhari and Muslim]
Does the Obligatory Ritual Bath (Ghusl) Suffice in Place of Ablution (Wuḍūʾ)?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
The more prudent course is to perform ablution (wuḍūʾ) after the ritual bath (ghusl), so as to exit the difference of scholarly opinion and because the sufficiency of the ritual bath in place of ablution is contingent upon a number of conditions and requirements being met. And Allah the Almighty knows best.
What is the ruling on the ablution of one who cuts his nails, and is it permissible to cut them before the ritual bath for major impurity (janabah)?
Cutting nails does not invalidate ablution, and it is permissible to cut them before the ritual bath for major impurity. And Allah the Almighty knows best.