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 on public street water if it gets on a person's clothes or body?
The default ruling is that public street water is pure (tahir). If one is certain of its impurity (najasa), then a small amount that gets on the lower part of a person's clothes or body is overlooked (excused). And Allah the Almighty knows best.
Does Laylat al-Qadr move between the nights of Ramadan?
Laylat al-Qadr is definitely in Ramadan, and it is most likely in the last ten nights, especially on the odd-numbered nights.
For this reason, the Prophet ﷺ commanded observing worship in the last ten nights, and he himself used to dedicate those nights to worship. Many people put special effort into the 27th night of Ramadan, and they are rewarded in any case, whether they actually coincide with Laylat al-Qadr or not, because worshiping on any night of Ramadan carries great rewards.
Does swallowing a fly, road dust, or flour dust break the fast?
A fasting person does not break their fast if something enters their body cavity against their will, such as a fly, road dust, or flour dust.