Can prayers and fasts left undone by a deceased person be made up on their behalf, and how are they counted if the number is unknown?

Summary

According to the majority of scholars, missed prayers of the deceased cannot be performed by anyone else. If the deceased had no chance to make up missed fasts due to limited time, illness, travel or other obstacles, the heirs bear no responsibility and no fidyah is due. If the deceased missed fasts and did not make them up when able, an heir may fast on their behalf though it is not obligatory; if not done, a fidyah of one cupak of rice per day must be taken from the estate. For counting, one who always fasted is not presumed to have missed any; one who always fasted Ramadan but fell ill is counted for the days of illness until death if death occurred in Ramadan; and one who never fasted is counted from puberty until before death.

Written in our own words from the original fatwa — check the source before acting on it.