Is it permissible for an elderly person who does not pray, and was blessed with Hajj yet became more averse to prayer and Allah's rulings, to live with female relatives whose hair he sees, and what should be done concerning him?

The supplication for guidance is prescribed in all circumstances. A person's insistence on abandoning prayer is one of the greatest sins, and it is considered apostasy by many scholars, even if the majority do not consider it an exit from the faith unless one deems its abandonment permissible. If he has not committed an act of disbelief, then treat him as a disobedient Muslim and advise him by reminding him of the punishment for abandoning prayer. If he responds, then all praise be to Allah; otherwise, you have absolved yourselves. There is no harm in him remaining with you and seeing your grandmother's hair if she is his wife or a mahram, as long as he has not exited the faith.