Is Zakat obligatory on money that has been agreed upon to be invested with profit or loss, but its operation has been delayed for three months, and if it is obligatory, is it calculated from the date of agreement or from the date of operation?

Money is subject to zakat if it reaches the nisab and a full year has passed on it, whether it is saved, shared, or for a specific purpose such as marriage or buying a house; because zakat is obligatory on money by virtue of it being money. If the money is shared, you pay zakat on your share along with its profit, and deduct the partner's share.