Is the niece considered a martyr for dying by burning as a result of a car bomb explosion, knowing that she remained in a coma for three days before her death, and that her husband (who died before her) belongs to a misguided sect that does not revile the Companions or distort the Quran? And is it permissible for her sister to pray on her behalf during the period of her coma?

If the cause of death was burning, then the woman is hoped to receive the reward of martyrdom, due to the Prophet's (peace and blessings be upon him) saying: "The one who dies by burning is a martyr."

As for the sister praying on her behalf, this is incorrect. It is not legislated for anyone to pray on behalf of another, whether alive or dead.

Shaykh al-Islam Ibn Taymiyyah said: "As for the obligatory prayers, no one prays on behalf of another. However, if one of them prays a voluntary prayer on behalf of the deceased and dedicates it to him, or fasts a voluntary fast on his behalf and dedicates it to him, that will benefit him."