Will a woman who dies without wearing a hijab remain in Hell forever, with Allah never forgiving her, and will she never smell the fragrance of Paradise? And will Allah cast into Hell one who dies ill without praying due to their inability to do so?

Neglecting the hijab (definition) is a major sin. The Prophet (peace and blessings be upon him) warned women who are "clothed yet naked" that they would not enter Paradise nor even perceive its scent. So, if a woman dies in this state but dies upon monotheism, her fate is subject to Allah's will; He may punish her if He wills, or He may forgive her if He wills. It is appropriate to seek forgiveness and supplicate for her.

As for prayer, it is not waived for a legally responsible person as long as their intellect is sound. If the sick person neglected it out of ignorance of its obligation, we hope that Allah will forgive them. But if they neglected it out of negligence, then they have exposed themselves to Allah's wrath and punishment. It is appropriate to seek forgiveness and supplicate for mercy and forgiveness for them, as long as they are among the people of monotheism.