Question: Can a person who is in charge of his own prayers and fasting perform the prayers and fasts of a person who has passed away?

Answer: As to prayers, there is no problem.
As to fasting, if one is hired to perform it, it is no problem while if one fasts on behalf of others without being hired; rather, he does so for free, by obligatory caution, the fasts are not valid. Of course, the eldest son can perform his late father's missed fasts in any case.