Is a cancer patient who uttered words doubting God's mercy due to her severe pain held accountable? And can expiation be made on her behalf for her inability to pray due to her health conditions that prevented her from ritual purity?

May Allah have mercy on your mother and forgive her. If words indicative of displeasure and frustration were uttered by her while she was unconscious due to severe illness, there is no blame upon her, for the Prophet, peace be upon him, said: "The pen is lifted from three: from the sleeper until he awakens, from the child until he grows up, and from the insane person until he regains his sanity or recovers." However, if she uttered them while she was in her full senses, then it is forbidden, and we ask Allah to forgive her. There is no specific expiation for this, but the reward of charity and supplication will reach her.

Regarding prayer, it is not waived for her as long as she is conscious. If she is unable to purify herself, others should help her. If she is unable to perform ablution (wudu), she should perform dry ablution (tayammum (definition)). If she is unable to pray standing, she should pray sitting. If she is unable to pray sitting, she should pray reclining. If she can only make gestures, then that is obligatory upon her. There is no specific expiation for her missing prayers, and it is not prescribed to make them up on her behalf. Rather, one should seek forgiveness for her and give charity on her behalf.