Is Zakat obligatory on two plots of land, one designated for residence and the other for trade, a year having passed without construction commencing on either, and on a third plot of land, which was purchased for a brother four years ago, but he was unable to pay its installments, and its price has since doubled?

There is no zakat on land you bought with the intention of dwelling, based on the hadith: "A Muslim is not obliged to pay zakat on his slave or his horse." As for land you bought with the intention of selling, zakat on it is obligatory upon the completion of a year (hawl) if its value reaches the nisab, because it is considered a trade commodity. As for the land you intended to transfer to your brother, your intention at the time of purchase and whether a contract was made between you and your brother must be clarified to determine whether zakat is obligatory on it or not.