How is the Zakat calculated for a down payment on an apartment that was returned and deposited in the bank, and is it subject to Zakat along with the original amount that will soon complete its hawl (one lunar year), or must it complete its hawl independently?

You must calculate Zakat from the time you possessed the nisab, not from the time you deposited it to buy the apartment. So, if you owned money in Muharram 1425 AH, then deposited it to buy an apartment which you were unable to purchase, Zakat becomes due on it in Muharram 1426 AH. It is not permissible to delay the disbursement of Zakat except out of necessity.