Is it permissible for a wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
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 it permissible for a wife to boycott (not to attend to his different needs) her husband?
It isn`t permissible for the woman to boycott her husband unless he is the reason behind that, and it is recommended that both spouses seek the advice of righteous people to make reconciliation.
Is it obligatory for a wife who has been abandoned for many years to observe the waiting period (iddah) after her husband passes away?
If her husband passes away, the wife is required to observe the waiting period (Iddah), even if he had abandoned her, because she is his wife and inherits from him, so she must observe the iddah after his death. And Allah Knows Best.