What is the ruling on swallowing saliva while fasting?
It is permissible for a fasting person to swallow their saliva because avoiding it would cause undue hardship and excessive strictness in religion. Islam discourages such excessiveness since Allah the Almighty intends ease for His followers and does not intend to put them in hardship.
What is the ruling of Islamic Law on continuity (muwalah) in the ritual bath?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Continuity (muwālāh) means washing each part of the body immediately after the previous one, without leaving a gap long enough for the first part to dry before the second is washed. According to the Shāfiʿī school, continuity is a recommended act (sunnah) in both the ritual bath (ghusl) and ablution (wuḍūʾ) — it is not obligatory.
It is stated in Nihāyat al-Muḥtāj ilā Sharḥ al-Minhāj: "Likewise, continuity in the ritual bath is recommended, just as it is in ablution."
Accordingly, continuity in the ritual bath is a sunnah. And Allah the Almighty knows best.
Someone wiped over his shoes after wearing them in a state of purity, then took them off and prayed without them?
Ablution is not invalidated by taking off leather socks or shoes after wiping over them. However, whoever takes them off after wiping must wash his feet only. If he prayed without washing his feet, he must wash his feet and repeat the prayer. And Allah the Almighty knows best.
What is the ruling on performing ablution (wudu') and ritual bathing (ghusl) with Zamzam water?
It is permissible to perform ablution and ritual bathing with Zamzam water. However, scholars disliked using it for cleaning after relieving oneself (istinja'). And Allah the Almighty knows best.