Should the installment sale price be fixed regardless of the down payment, or can it vary based on the down payment and the repayment period, in order to determine the installment amount according to the buyer's ability, without needing to mention two absolute prices for cash and installment?

It is permissible for a person to sell his commodity for a known term and at a price higher than its immediate cash price. It is also permissible for him to increase or decrease the installment amounts based on the buyer's situation and the down payment, as the fundamental principle in contracts and transactions is permissibility unless there is a Sharia-based prohibition.