Is it correct that everything dry is pure even if it has impurity on it?
If something impure becomes dry, it remains impure and is not purified by drying. However, the impurity does not transfer by touching it if the one touching it is also dry. And Allah the Almighty knows best.
Should nail polish be removed before making ablution?
Yes, it should be removed because it prevents water from reaching the nails.
If a traveler settles or a sick person recovers while fasting, is it permissible for them to break their fast?
● If a sick person starts the day fasting and then recovers during the day, they must complete their fast.
● If a traveler starts the day fasting and then settles (returns or stops traveling) during the day, they must also complete their fast.
● It is forbidden for both of them to break their fast because the concession (rukhsah) is no longer valid once its reason disappears.
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.