Is borrowing from a bank to purchase a car, in exchange for a deposit with interest, with part of the installment paid from the deposit's interest and the remainder in cash, considered permissible by Sharia and free from the suspicion of usury, and how is Zakat calculated on wealth in this case?

If the bank is Islamic and the investment deposit is mortgaged against a debt, and the profit is not guaranteed but the bank is given the agreed-upon percentage of the profit (if it occurs), and the debtor completes the monthly installment amount, then there is no harm in that. Pledging deposits is permissible, provided that the account holder is prevented from disposing of them throughout the duration of the pledge. If the bank is the mortgagee, then the amounts must be transferred to an investment account so that the guarantee is negated and the account holder becomes entitled to their profits. As for Zakat, the investment deposit is subject to Zakat as trade goods after deducting the equivalent of the remaining debt, provided that one does not have non-Zakat-eligible wealth exceeding their needs that could cover the debt. If, after deducting the debt, there remains nothing that reaches the Zakat threshold, then there is no Zakat due at that time.