Is it permissible for a wife to leave her house without asking her husband?
It is impermissible for the wife to leave her house without asking her husband except for a sound reason.
What is the ruling on taking a medication tablet sublingually during the daytime in Ramadan?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Taking a medication tablet sublingually (under the tongue) during the daytime in Ramadan does not invalidate the fast, since it does not reach the internal cavity (al-jawf) through an open passage.
However, if the tablet dissolves and any part of it is swallowed, then the fast is broken.
And Allah, the Exalted, knows best.
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.
What is the ruling of Islamic Law on supplicating with other than the transmitted (Ma'thur) supplications in prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to supplicate (make du'a) during the prayer for anything from the affairs of religion or worldly life, and the prayer is not invalidated by doing so.
Shaykh al-Islam, the Imam an-Nawawi, may Allah have mercy on him, says: "Our madhhab [i.e., the Shafi'i madhhab] holds that it is permissible for a person to supplicate during it [the prayer] with anything that is permissible to supplicate with outside the prayer, from the affairs of religion or worldly life. He may say: 'O Allah, grant me wholesome sustenance, offspring, a house, and a beautiful young wife' — describing her; or: 'O Allah, free so-and-so from prison,' or 'destroy so-and-so,' and other such things — and none of this invalidates his prayer according to us. And this is also the view of Malik, ath-Thawri, Abu Thawr, and Ishaq." [Al-Majmu', Vol.3/P.454]. And Allah, the Exalted, knows best.