What is the ruling on a second congregation [being formed] in the mosque?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
It is disliked to deliberately seek to establish a second congregation in a mosque that is not one frequented by transient passersby — such as a neighborhood mosque with a regular, appointed imam — unless permission is granted by that imam, since doing so implies criticism and an affront to him. However, if the mosque is one frequented by transient passersby — such as mosques located in marketplaces — then a second or even third congregation is permissible there, whether or not it has a regular, appointed imam, and whether or not that imam gives his permission. This is because such mosques experience a continuous flow of people coming and going, so no implication of criticism toward the imam is perceived in the formation of multiple congregations in that setting. And Allah, the Exalted, knows best.
Is it permissible to pay the Fitr Zakah (obligatory charity) of Ramadan on behalf of a dead person?
The Fitr Zakah of Ramadhaan isn`t due on one who had passed away before the sunset of the last day of Ramadan. 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.
What is the ruling on wiping the white area behind the ears instead of wiping the head?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. Wiping the white area behind the ears suffices for that. And Allah the almighty knows best.