Is it permissible for a woman in her waiting period (Iddah) after her husband's death to leave her house and mix with non-Mahrams?
It is not permissible for a woman in her waiting period (Iddah) after the death of her husband to leave her house except for a necessity, such as for medical treatment, nor is she allowed to mix with non-Mahrams. A woman is not permitted to mix with anyone other than her husband or Mahrams, whether she is in her waiting period or not. However, there is no harm in accepting condolences from those who visit and responding to their inquiries about her well-being. And Allah Knows Best.
What is the ruling on visiting a deceased's grave and supplicating Allah for him by his wife? Is the reward of reciting verses of the Holy Qur'an reaches the deceased?
There is no harm on visiting graveyard by woman with the intention of piety so long as they are dressed in accordance to the Islamic teachings. We ask Allah, The Almighty that the reward of reciting the Holy Qur'an on dedicated to the deceased reaches him. And Allah Knows Best.
Is committing Zina (Adultery and extramarital sex) without the intention of getting pregnant or deflowered considered full Zina?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The Messenger of Allah (PBUH) says: "The eyes commit fornication, the hands, the feet, and the private parts." [Musnad Ahmad, P.3912]. Sheikh Shu`aib `Arn`oot graded this Hadith as sound. What you are asking about is far graver. Generally speaking, sincere repentance erases sins, good deeds erase bad deeds, and fearing Allah stops one from committing this heinous act. In addition, the devil is man`s worst enemy and whoever surrenders themselves to the wolf will be eaten. And Allah The Almighty Knows Best.
Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?
The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).