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.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.
What is the ruling on performing the Witr prayer as a single rak`ah?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible to perform the Witr prayer as a single unit (rak‘ah). It was narrated from Ibn ‘Umar that a man asked the Messenger of Allah ﷺ about the night prayer, and the Messenger of Allah ﷺ replied: 'The night prayer is offered two by two (mathna mathna). If one of you fears the approach of dawn, let him pray a single rak‘ah to make what he has prayed odd-numbered (Witr) for him.' (Related by al-Bukhari & Muslim)). However, limiting the prayer to only one rak‘ah is considered 'contrary to the preferred way' (Khilaf al-Awla).
It is stated in Al-Minhaj al-Qawim Sharh al-Muqaddimah al-Hadramiyyah (p. 137): 'The minimum of Witr is one rak‘ah, but limiting it to that is contrary to what is best.'
The most complete form of Witr is eleven units, while the minimum level of 'perfection' is three units. It is stated in ‘Umdat al-Salik (p. 60): 'The minimum of Witr is one rak‘ah, and its maximum is eleven, performing the taslim (salutation) after every two units. The lowest level of perfection is three units with two separate taslims (meaning 2+1).' And Allah the Exalted knows best.
Is it a condition that a woman should untie her locks while making Ghusl (ritual bath)?
Ghusl from Janabah (ritual impurity), or menstruation obligates that water reaches the roots of the hair in order for the Ghusl to be valid, but if it doesn`t, then hair locks must be untied for water to reach them, and for Ghusl to become valid.