What is the ruling on feeding a needy person for each day for a mentally ill wife who missed 28 days of Ramadan due to her illness, and she refuses to feed and insists on making up the days, and is it permissible to feed them all at once without her knowledge?

If fasting causes weakness and emaciation to a woman, then she may break her fast; otherwise, she may not. The criterion is the feared harm. If she breaks her fast, the default is that she must make up the days (qada'), and feeding the poor (it'am) is only resorted to when there is despair of being able to make them up. Assuming that it is permissible to transition to feeding the poor, it is not sufficient to feed on her behalf without her permission, and it is permissible to feed the poor all at once.