Is it obligatory to act upon the father's will after his death regarding the prohibition of photographing his daughters, and what is the ruling on refraining from issuing national identity cards for this reason?

It is more cautious to avoid photography. The father's will in this regard should be carried out if its intent is to avoid non-essential photography, based on the hadith: "Is there any righteousness left for me to show my parents after their death?" It states: "Fulfilling their covenants after them." As for the national ID photo, it is a necessity, and there is no obligation to fulfill the father's will to prevent it due to the extreme hardship involved.