Does divorce occur with the statement: "Divorce upon me if you don't sell the car and give me half the money," knowing that I have not yet consummated the marriage with my wife, and is she required to observe 'iddah if the divorce occurs?

What you have uttered is an oath to divorce your wife conditioned on your brother selling the car and giving you half the money. If your brother fulfills your oath, your wife is not divorced. If he does not fulfill it, and you intended a specific time period, then no breach occurs until that period expires. If you had no intention, then scholars differ: The view of the majority is that the divorce does not become binding until there is despair of the car being sold (such as the person's death or the car being damaged). According to the Malikis, you are prevented from your wife until the car is sold and half its price is paid to you. Your wife can refer her case to a judge, who will set a period for ila' (vow of abstention). If four months pass and the sale has not occurred, you will be ruled divorced if your wife requests it. Shaykh al-Islam Ibn Taymiyyah said: Only an expiation for an oath is binding upon you, and no divorce, if you did not intend divorce. In the event of divorce, it is an irrevocable divorce (ba'in) because it occurred before consummation, so your wife is not permissible for you except with a new marriage contract. As for ihdad (mourning period), the prevalent fatwa with us is that ihdad is binding upon a widow. Some scholars hold that it is binding upon a woman irrevocably divorced. On both views, there is no ihdad for your wife because she is either not divorced or divorced before consummation, and a woman divorced before consummation has no iddah (waiting period).