What should a person who was favored from Allah with a newborn, but couldn`t afford an Aqeeqah, do?

Aqeeqah(the sheep slaughtered on the seventh day from the child`s birth) is a desirable Sunnah for the financially able since Allah, The Exalted, charges not a soul beyond its capacity. Therefore, if the father couldn`t afford the Aqeeqah before the end of his wife`s confinement, then it isn`t due on him, and if he was able to afford it later on, then it is permissible, but if he didn`t until the child reached puberty, the latter can offer the Aqeeqah himself.

What is the ruling on the mother who resorts to practitioners of witchcraft to make her son hate his wife?

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.

What she is doing is forbidden and amongst the seven destructive sins. Hence, she must make repentance, seek forgiveness from Allah, regret what she has done and adhere to the teachings of Sharia. And Allah The Almighty Knows Best..

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 Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?

Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.