What is the ruling on istinja' after urination, and is it done with water and soap or with water only?
Istinja' from urine and stool is obligatory. It is permissible to perform istinja' with water alone, or with toilet paper alone. The best way is with toilet paper then water. If one wishes to suffice with one of them, then water is better. And Allah the Almighty knows best.
What is the ruling on praying in congregation at the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Congregational prayer (Salat al-Jama‘ah) is a communal obligation (Fard Kifayah) for resident men regarding the performance of the prescribed (obligatory) prayers. For men, praying in congregation at the mosque is better than praying elsewhere, such as at home. On the authority of Abdullah bin Umar, the Messenger of Allah ﷺ said: 'Prayer in congregation is twenty-seven degrees more excellent than the prayer of a person alone' (Reported by Bukhari & Muslim). Furthermore, on the authority of Abu Hurayrah, the Messenger of Allah ﷺ said: 'Shall I not tell you that by which Allah erases sins and raises ranks?' They said, 'Of course, O Messenger of Allah.' He said: 'Performing wudu thoroughly despite difficulties, taking many steps toward the mosques, and waiting for the next prayer after the prayer; that is your Ribat (steadfastness)' (Narrated by Muslim).
As for a woman, her praying in congregation at home is better for her than in the mosque, according to the saying of our Master the Prophet ﷺ: 'Do not prevent your women from attending the mosques, but their homes are better for them' (Narrated by Abu Dawood). Young boys should be encouraged to attend the mosques and congregational prayers so they may become accustomed to them. And Allah the Exalted knows best.
Does passing wind, from the anus without a smell, invalidate prayer?
If a person is certain of having passed wind even if it was with no smell, then both his/her ablution and prayer are invalidated, thus he/she should remake ablution and re-perform prayer.
What is the Islamic ruling on one who was unable to fast and then regained the ability?
He is not required to make up the fast (Qada) even if he becomes capable of it; whether he regained the ability to fast after paying the fidya (feeding a needy person for each day of missed fasting) or before it, because he was liable for paying it in the first place, so it remains binding upon him. However, if he delayed paying it beyond the first year, nothing is required of him due to the delay. If he is unable to pay it, it does not remain as a debt upon him. And Allah the Exalted knows best.