Is it permissible to offer the Eid sacrifice in a non-Muslim country?

Eid sacrifice is permissible anywhere, and Islamic Sharia hasn`t determined that it should be in an Islamic country, but poor Muslims should be given a share in order for it to be valid since it is an act of worship. A portion of that Eid sacrifice should be given at least to one poor Muslim, and if that wasn`t possible then the one offering it should consume it along with his family.

Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?

It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.

Does the deceased hear the supplications or recitations of those visiting his/her grave? And does making constant supplications for the deceased who didn`t adhere to performing the prescribed prayers ameliorate his/her affliction?

Praise be to Allah the Lord of the Worlds.

In principle, the dead hear the living since it has been rigorously authenticated that the Prophet (peace and blessings be upon him) ordered the bodies of the idolaters slain in the Battle of Badr to be buried. He then approached them and called them one by one and said, “Have you found what your Lord promised to be true for we have found what our Lord promised us to be true.” ‘Umar asked him, “O messenger of God! Why do you speak to lifeless bodies?” The Prophet (peace and blessings be upon him) replied, “By the One Who has sent me with the truth! You do not hear my words better than they do except that they cannot respond.”{Related by Bukhari & Muslim}.

However, not all the deceased are in the same situation because Allah the Almighty says, "Before them is a Partition till the Day they are raised up."{Al-Mu`minun, 100}. Moreover, supplication reaches the deceased. And Allah 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).