Should the organs of the deceased mother be donated based on her will, and is delaying the donation considered a sin, knowing that the organs would have already died upon death? And is the mother considered a martyr if she dies due to a medical error during surgery?

Regarding the death of a deceased person's organs, it is referred to specialist doctors. If your mother's will to donate her organs was valid, then there is no blame on you for your lack of knowledge and unintentional violation. This is if the validity of the will is upheld, otherwise, some jurists invalidate it because they deem organ donation impermissible in principle.

As for your mother's death due to a doctor's error, it is hoped that she will receive the reward of martyrdom, not because of the doctor's error, but because of her death during her surgery. Every death a Muslim experiences is considered martyrdom, and there are varying degrees of martyrdom.