Is the wife entitled to demand the apartment's down payment in gold, to be calculated at its current price, especially after her refusal to move into it, given that she paid part of its price and the husband wishes to move into it and terminate the contract for the other apartment?

The wife does not have the right to demand half the price of the apartment. Rather, she is entitled to her right in one of three ways: either she lent this amount, in which case a similar amount must be returned to her; or she participated with it in the apartment, in which case she has a share in its value equivalent to what she paid; or she agrees to move into it, live in it, and terminate the contract for the other apartment.