What is the ruling on performing the standing (qiyām) and bowing (rukū‘) portions of the prayer normally, while performing the prostration (sujūd) seated due to knee pain?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If performing sujūd (prostration) in prayer causes the worshipper pain in the knees, then it is permissible for him to perform it through gesture (īmā') while seated, since Allah, Glorified and Exalted is He, has lifted hardship from His servants. On the authority of ‘Imrān ibn Ḥuṣayn (raḍiyallāhu ‘anh), he said: "I suffered from hemorrhoids, so I asked the Prophet ﷺ about [how to perform] the prayer, and he said: 'Pray standing; if you are unable, then sitting; and if you are unable, then on your side.'" [Ṣaḥīḥ al-Bukhārī]
If the valid excuse later subsides, the worshipper is then obligated to perform the prayer with all its pillars and conditions fully observed — including standing, rukū‘ (bowing), and sujūd (prostration). And Allah, the Exalted, knows best.
What is the ruling on water present on the floor of a toilet/bathroom?
The default ruling is the purity of this water present on the bathroom floor. If one is certain or strongly suspects its impurity, then one washes whatever part of the body or clothing this impure water has touched. If one doubts its impurity, the default is purity, and we do not rule it impure based on mere doubt. And Allah the Almighty knows best.
What is the ruling on ablution without istinja' after sleep?
The sleep of one whose buttocks are not firmly seated on the ground invalidates ablution. Whoever wakes up and wants to pray must perform ablution only. Istinja' is not a condition for the validity of ablution, because it is for removing impurity from the private part. If there is no impurity on the private part, then istinja' is neither obligatory nor recommended. And Allah the Almighty knows best.
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.