What is the ruling if someone wipes his head then shaves it - must he repeat it?
If a person performing ablution shaves his head after wiping it during ablution, he is not required to re-wipe his head or repeat the ablution. And Allah the Almighty knows best.
Is it permissible for a wife to give her money to her family as a charity, or a gift without asking her husband, or seeking his consent?
The wife has the right to give her money as a charity, or a gift to her family, or to other people after consulting her husband out of respect, and this is the meaning of treating on footing of kindness and equity. Therefore, if he wanted to stop her from helping her family, then there is no harm in not telling him.
Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?
A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.
What is the ruling on fasting the six days of Shawwal?
Fasting the six days of Shawwal is Sunnah. The Prophet ﷺ said: "Whoever fasts Ramadan and then follows it with six days of Shawwal, it is as if they have fasted for a lifetime." [Narrated by Muslim]
This is because fasting one month of Ramadan is rewarded as fasting for ten months, and the six days are equivalent to sixty days, completing a full year of fasting.
