Is it permissible for a person to give the Zakah (obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and none provided for particularly by whom are obliged to provide for her. And Allah 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.
How many rak‘ahs are there in Tarawih prayer?
The most complete form of Tarawih prayer consists of twenty rak‘ahs, excluding Shaf‘ and Witr. This is the opinion of the majority of scholars, both past and present, and it is the practiced tradition in the two Holy Mosques.
However, Tarawih is valid with any even number of rak‘ahs, even two rak‘ahs, as long as it is performed with the intention of Qiyam al-Ramadan.
When is supplication (du‘a) more likely to be accepted: before or after breaking the fast in Ramadan?
Du‘a is accepted at all times, and this is part of Allah’s mercy and generosity toward His servants.
The Prophet ﷺ said: "No Muslim makes a supplication that does not involve sin or severing family ties except that Allah grants them one of three things: either He grants their supplication immediately, or He stores it for them in the Hereafter, or He averts from them an equivalent harm." [Narrated by Ahmad]
However, in Ramadan, du‘a is especially likely to be accepted shortly before breaking the fast.
The Prophet ﷺ said: "Three supplications are never rejected: the supplication of a fasting person until they break their fast, the supplication of a just leader, and the supplication of an oppressed person. Allah raises it above the clouds, opens the gates of heaven for it, and says: ‘By My might, I will surely grant you victory, even if after a while.’" [Narrated by Al-Tirmidhi]