Is zakat obligatory on a plot of land purchased for the purpose of building and selling apartments, knowing that construction has not yet begun? And if it is obligatory, should it be paid on the day of Arafat, as the questioner is accustomed to, or after six months, on the date the money was collected?

The apartment intended for ownership is not subject to Zakat (definition), and a sudden intention to trade it does not affect this. As for the rest of your share of the land, ascertain its value at the end of the year, deducting any debts you owe, including half the borrowed price of the land. If you have surplus wealth beyond your basic needs from funds not subject to Zakat, use it to offset the debt and pay Zakat on all your wealth. If a person has borrowed money and repaid it, or has non-Zakat-eligible wealth that covers their debt, then a new year (for Zakat calculation) begins for this loan because it is wealth acquired from a non-growing principal.