How is zakat calculated on invested money and on an apartment that generates income but is designated for demolition and reconstruction? And are the amounts paid to help relatives considered from zakat?

You have not clarified the nature of the investment in contracting to determine how its Zakat (definition) is calculated. However, you must enumerate your capital and profits to determine the Zakat due from you. As for your assistance to your mother-in-law in purchasing the apartment, if you paid the money with the intention of Zakat and your mother-in-law is one of its eligible recipients, then it is permissible. Otherwise, it is not sufficient.