Is my mother, who is unable to perform the prayer with ablution, bowing, prostration, and recitation, obligated to pray, or is it waived for her?

Prayer is not waived for the elderly as long as their intellect is present. They should pray according to their ability: standing, sitting, on their side, or lying down, indicating with gestures. If they are unable to gesture, they should perform the actions with their hearts. However, if intellect is lost due to dementia and the woman reaches a state where she does not comprehend what she is saying, then the pen is lifted from her. Her family must assist her with purification and prayer at its appointed time, and they will be rewarded for that.