What is the ruling regarding someone who intended to offer a cow as a sacrifice (Udhiyah) but was unable to slaughter it until the time for slaughtering had passed? Is he then obligated to slaughter it afterwards, and would it still count as an Udhiyah?

The Sunnah is for the sacrificer to slaughter his sacrificial animal with his own hand. If the time for slaughtering, which is sunset on the third day of Tashreeq, has passed, then he has missed the Sunnah of the sacrifice and its reward. It is not obligatory to slaughter it then, unless it was made obligatory by a vow or designation. He may then donate it, distribute it, or do whatever he wishes with it. If it was a voluntary sacrifice and its time has passed, then he has missed the Sunnah of the sacrifice. As for an obligatory sacrifice, it should be slaughtered as a make-up. Whoever withholds his sacrifice until its time has passed commits a sin for missing the reward of the Sunnah, and he may do with it whatever he wishes.