Does buying meat equivalent to the weight of a slaughtered animal and distributing it avail for an udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
That does not avail for the sacrifice (uḍḥiyyah), because the sacrifice necessarily requires slaughtering an animal from the category of anʿām (camels, cattle, and sheep/goats) within a specified time.
Rather, that is considered a form of charity (ṣadaqah) for which one is rewarded, but not an udhiyah. And Allah 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 an animal that results from crossbreeding between two types of livestock (an'ām) valid [for sacrifice]?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
An animal that results from crossbreeding between two types of livestock (an'ām) is valid [for sacrifice], with consideration given to the higher of the two required ages. Thus, in the case of an animal crossbred between sheep (ḍa'n) and goats (ma'z), only one that has reached two years of age is valid [for sacrifice]. And Allah, the Most High, knows best.
What is Aqeeqah?
It is the sheep slaughtered on the seventh day from the child`s birth, and it is a confirmed Sunnah after the Prophet (PBUH).