Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.
What is the ruling on someone who perform their prayer after finishing it because they believe they missed a Rak'a, a prostration, or that they did not perform it correctly (thinking their prayer was invalid)?
If he was sure that his prayer is void then reperforming it is an obligation along with figuring out the reason of invalidity so long as this wasn't out of uncertainty. And Allah Knows Best.
What is the ruling of Sharia on a Muslim woman who committed Zina with a Christian and became pregnant as a result?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
Abortion is forbidden in Islam as it entails taking the life of a soul unjustly. Rather, it is one of the major sins; however, it is permissible only when there is well-established danger on the mother`s life; in which situation scholars gave priority to her life over that of the foetus, since this is, according to Sharia: "The lesser of two evils". In case a Muslim woman committed Zina (Adultery) with a Christian and got pregnant, if this did happen, then this question should be presented to the Iftaa` Committee with the presence of the questioner herself. She could also ask a reliable scholar face to face or via phone. If she gives birth to the baby, then he/she is a Muslim and takes the name of his mother; not the name of the man who was a reason for its conception. And Allah The Almighty Knows Best.
I took a car from the Orphans' Fund Development Institution; is there usury (Riba) involved in this transaction?
If the Sharia's conditions were met, then there is no harm in this. And Allah The Exalted Knows Best.