As a divorced mother, is it permissible for me to take out a loan to pay off debts and purchase essential items such as a water heater and a washing machine, especially since the cost of the loan is less than purchasing in installments? And will this incur interest?

It is permissible to take a loan if it does not involve usurious interest. As for a usurious loan, it is not permissible except in cases of extreme necessity that entail significant harm, such as imprisonment. What was mentioned about purchasing a water heater and a washing machine does not permit borrowing with usury. And whoever fears Allah, avoids His wrath, and seeks His help, He will provide for him from where he does not expect.