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.
Is it true that whatever is dry is pure even if there was impurity on it?
The impure material object does not soil (make impure) anything else unless the impurity is wet and transferable. But, if the impurity is dry or non-transferable, then there is no problem. Fuqaha has stated that: There is no disagreement between Muslim scholars that when a dry impurity touches something dry it does not make the latter impure.
Does offering Udhiyah (Offering a Sacrificial animal at Aid Al-Adha) avails from offering Aqiqa?
Offering an Udhiyah doesn't avail a person from offering Aqiqa because each of which is a different act of worship. And Allah Knows Best.
It was found out that a man divorced his wife for the third time in 2005, but they continued cohabiting as man and wife. However, when they realized that what they were doing was unlawful, they came the Iftaa` Department in 2009 and were told that they can`t be together. What is the position of Sharia on this couple?
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.
Her Iddah* period starts after the third divorce. As for the continued cohabitation, it is unlawful because being ignorant about the rulings of Sharia while in Dar Al-Islam* is no valid excuse. If a baby came as the fruit of this unlawful consummation of marriage, then a judge of Sharia has the final say in this regard because lineage is a serious matter. And Allah The Almighty Knows Best.
* ʿIddah: a specified period of time that must elapse before a Muslim widow or divorcee may legitimately remarry. The Qurʾān (Sura,2/verse,228) prescribes that a menstruating woman have three monthly periods before contracting a new marriage; the required delay for a nonmenstruating woman is three lunar months.
* Dar Al-Islam: designates a territory where Muslims are free to practice their religion, though this often implies the implementation of Islamic law, whereas Dar al-Harb represents those lands ruled by non-believers