What is the ruling of Sharia on dealing with a house that was purchased through a long-term loan system with interest, with the option of selling it and getting rid of the interest, or continuing to pay the monthly installments which increase as the term lengthens?

The transaction through which the house was purchased is unclear. However, if the contract was a lease ending in ownership (ijarah muntahiyah bi al-tamleek), then it is invalid, and the house remains the property of its owner, who is entitled only to the market rental value (ujrat al-mithl). Any excess payment must be returned to the buyer. If, on the other hand, the contract was an interest-bearing loan (qard ribawi) or an installment sale with a late payment penalty clause, then the amount due must be paid without the interest or penalty. If you are compelled to pay them, they will bear the sin thereof, and you are not obligated to sell the house. Repentance is sufficient for those who directly engaged in or assisted with the contract.