What is the ruling on performing istinja' after passing wind from the anus?
Ablution is invalidated by passing wind from the anus, even without a smell. Only ablution becomes obligatory from it. Istinja' is not obligatory nor recommended. And Allah the Almighty knows best.
What is the ruling of Islamic Law regarding one who slaughters a ewe and it turns out to have been pregnant, and is it permissible to slaughter the ewe if one knows it is pregnant?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a person slaughters a ewe and it turns out to have been pregnant, the fetus becomes lawful (ḥalāl) by virtue of its mother's slaughter (tabaʿan li-ummihā).
It is stated in Mughnī al-Muḥtāj (Vol.6/P.158): "A fetus found dead [after the mother's slaughter], or found alive but in a state resembling that of a slaughtered animal [i.e., dying shortly after], becomes lawful — whether or not it had grown fur — provided it is found in the womb of a mother that was lawfully slaughtered, whether her slaughter was by cutting the throat, or by an arrow or hunting dog sent after her. This is based on the ḥadīth: 'The slaughtering of the fetus is [effected by] the slaughtering of its mother' [narrated by al-Tirmidhī, who graded it ḥasan, and by Ibn Ḥibbān, who graded it ṣaḥīḥ] — meaning that the slaughter which rendered the mother lawful renders the fetus lawful as well, by virtue of following her; and because the fetus is one of her constituent parts, and her slaughter renders lawful all of her parts."
This ruling differs, however, from the case of one who knows from the outset that the ewe is pregnant [and intends to sacrifice her specifically as the udḥiyah while pregnant] — in which case, according to the Shāfi'ī school, she does not fulfill the requirement of a valid sacrifice.
It is stated in Ḥāshiyat al-Bujayrimī 'alā al-Khaṭīb (Vol.4/P.335): "A pregnant animal does not fulfill the requirement [of a valid sacrifice], and this is the authoritative position (al-mu'tamad), because pregnancy diminishes the quality of the meat. As for why such an animal is nevertheless counted as complete [i.e., fully valid] in matters of zakāh, that is because the intent there is reproduction (nasl), not the quality of the meat.". And Allah, the Most High, knows best.
Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.
Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?
It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.