Is it permissible to take the amounts spent on the apartment at its old value or its current value? Is it permissible to take the amount in dollars at its old exchange rate or at today's rate? Is it permissible to give a married sister an amount to buy an apartment?

It is permissible for parents to revoke a gift they did not intend as charity, unless the children have married, the gift has passed out of their possession, they have altered it, or incurred debt based on it. This is based on the Prophet's (peace be upon him) saying: "It is not lawful for a man to give a gift and then take it back, except for a father with regard to what he gives his child." In the case of your question, the mother does not have the right to revoke the apartment she gifted to you without your consent, because you made significant alterations to it before she attempted to reclaim it. Thus, the mother's right to reclaim the apartment has been lost due to the alterations made. If you relinquish the apartment, you have the right to reclaim the money you spent on it, without consideration for market fluctuations or currency appreciation and depreciation. As for gifting to a married daughter or anyone else, it is permissible according to Islamic law, and equality among children in gifts is obligatory.