Is it permissible for children and the daughter-in-law to fast on behalf of the mother to compensate for the days of menstruation she missed, or for the household members to fast on her behalf and for her to be responsible for their iftar, or for her to send juices to the mosque for breaking the fast of those who are fasting?

You must repent for any shortcomings in learning the rulings of Islamic law, count the days you missed fasting, and make them up. It is not permissible to resort to feeding the poor, nor to fast on behalf of another. If there is no legitimate excuse preventing you from making up the fasts, then you must make them up according to your ability, even on short days, as long as it does not harm your body. If you are completely unable to fast due to an illness from which there is no hope of recovery, or due to old age, then you are obligated to feed one poor person for each day, and the food must be given to the poor. Juices and similar items are not sufficient.