Is the plaintiff considered sinful and does she owe expiation and repentance after she vowed to God to abstain from eating coal, then resumed eating it when she learned it was not harmful?

What the questioner mentioned, that she uttered, "I pledge to God that I will not do such and such," is a matter upon which scholars have differed. The preponderant opinion is that it is not an oath. However, a Muslim should fulfill their pledge, based on the Almighty's saying: "And fulfill the covenant of Allah when you have covenanted," and "And fulfill the covenant; indeed, the covenant will be questioned." And due to the Prophet's (peace be upon him) saying: "There is no religion for one who has no covenant." Therefore, one must generally observe their covenants, especially those made with God, as long as they do not involve disobedience.