What is the ruling on purchasing mobile phones or other goods by installment, and what is the way out for someone in dire need who does not possess their cash price, if that is forbidden?

There is no harm in purchasing goods by installments from their owner, even if the price is higher than their cash price, because the deferment period has a share in the price. Installment selling is among the permissible forms of selling in transactions where immediate قبض (delivery and taking possession) is not a condition, provided that no interest is stipulated for late payment, and the contract is made for a specific, known price.