Is it permissible to pay expiation for the days one broke their fast in Ramadan due to doubt, by estimating it as the full number of days in the month, and appointing an orphanage and widow care center to pay the financial amounts, even if the person in charge of the center is not completely trustworthy?

If your fasting and breaking fast times are mixed up due to doubt about the validity of the fast because of committing sins, then know that this is not an excuse to intentionally break the fast. The fast is valid, though with reduced reward, and you must repent and make up for it.

If you broke your fast without engaging in intercourse, you must repent and make up for it. Feeding the poor does not suffice for making up the fast; rather, feeding the poor is only required if you delay making up the fast until another Ramadan.

If you broke your fast by engaging in intercourse, you must repent, make up for it, and offer expiation in the following order: freeing a slave, and if you cannot find one, then fasting for two consecutive months, and if you are unable to do so, then feeding sixty needy persons.

Your obligation for feeding the poor is not discharged by paying the amount to someone you know is untrustworthy, because your liability remains occupied with doubt about whether the food will reach those entitled to it. It is a condition that the agent must be trustworthy.