I used artificial nails on my wedding night, but I was surprised to find out that they require at least a week to remove. However, I performed all my prayers during that period. What is the ruling on those prayers?
If these nails prevent water from reaching one's skin then your prayer are invalid and obliged to redo all of them. And Allah Knows Best.
I`m a university student. While I was sitting for an exam, the professor caught my fellow student cheating. I heard him telling her to hide the dossier. After the exam, he asked me to testify that I saw her cheating although I heard him telling her to hide the dossier but didn`t see her cheating. 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.
It was narrated that the Prophet (PBUH) said to a man: "Do you see the sun?" He replied: "Yes." He said: "Give witness in a similar case [which is as clear as the sun], or leave it." [Reported by Al-Baihaqhi in "Sho`ab Al-Eman" pp.10964]. Therefore, it is not permissible to testify about something that you haven`t actually seen. And Allah The Almighty Knows Best.
Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
Is it permissible to fast on behalf of the dead who died owing missed fast to make up?
His relative should fast on his behalf, and it is permissible for the guardians to give permission to non-relatives of the dead to fast on his behalf as well. And Allah Knows Best.