What is the ruling on a Muslim who slaughters an animal while being in a state of Janabah (ritual impurity)?

All Perfect Praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upo all of his family and companions.

Slaughtering is permissible for the ritually impure man and the menstruating woman because ritual purity isn`t a condition for the validity of the slaughtering. Moreover, it is permissible for the uncircumcised person to do the slaughtering as well. And Allah The Almighy Knows Best.

Is it incumbent on a father to cover the marriage costs of his son if the latter couldn`t afford them?

The son should seek the help of his relatives in order to convince his father to do the aforesaid, and the father should make sure that his son doesn`t commit fornication through helping him to get married, and Allah will reward him for doing so.

Is it permissible to donate corneas to Jordan Eye Bank or all the organs via telephone?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Corneas donation that is carried out after one's death is permissible by the Board of Iftaa'. Because this procedure is highly sensitive, the donation process

should undergoes to an accredited mechanism. And Allah, The Exalted, Knows Best  

Is it permissible for a woman in her menstrual period to recite from the Mus-haf (copy of the Quran ), or to recite by heart?

A menstruating woman is permitted neither to recite nor to touch the Quran according to what Ali Bin Abi Talib (May Allah be pleased with him) reported about the Prophet (PBUH) who was only held from reciting the Holy Quran by Janabah (Major impurity) [Al-Tirmizi in a sound Hadith]. Although Janabah and menstruation are major impurities, a menstruating woman is permitted to supplicate Allah (Duaa`) and make Zikr (Tasbihat ), even if these involved saying words from the Holy Quran, provided that she does not mean the words for themselves but as a supplication, or Zikr. Moreover, she is rewarded for not reciting the Quran during her menstrual period because she abided by the injunctions of Allah.