Does bleeding from the body, such as from wounds, invalidate ablution?
Bleeding doesn't invalidate person's ablution. And Allah Knows Best.
Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.
An Arab young man had an illegitimate sexual relationship with a Christian American while she was staying in one of the Arab countries. After she returned to America, she told him that she had doubts that she was impregnated by him. It is worth pointing that it is hard for him to get a visa to the USA. What is the ruling of Sharia on this?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Zina (Adultery and extramarital relations) is one of the grave sins that incur the wrath of Allah if the adulterer didn`t make immediate repentance. However, the child isn`t attributed to the adulterer. Rather, he/she is attributed to the woman who got pregnant by him and, according to Sharia, it isn`t considered a legitimate child of the adulterer. And Allah The Almighty Knows Best.
Is it permissible for someone who has forgotten to mention the supplication pertaining to answering the call of nature to say it while in the toilet?
It is disliked for a Muslim to mention Allah while in the toilet, but he/she may recall the supplication in his/her head without uttering it; that is in case he/she had forgotten mentioning it before entering the toilet.