Is she considered sinful, the one who bought a golden necklace in installments and did not receive it until after paying the full amount to the seller, who kept it for a week?

Purchasing jewelry with deferred payment is not permissible, based on the hadith: "Do not sell gold for gold unless it is like for like… and do not sell from it that which is absent for that which is present." Currency takes the place of gold. If the questioner knew the ruling before the sale, she is sinful and must repent. If she did not know, then there is no sin upon her. In any case, the contract that involved delaying the payment is invalid, so the questioner does not own the necklace, nor does the seller own the price. A new contract can be made for the necklace, and the questioner should pay the remaining price, with the previously received amount being accounted for.