What is the wisdom behind killing children and the elderly in times of war and disaster, given that they do not participate in the fighting, and why does Allah take their souls?

It is not permissible for a Muslim to object to the actions of Allah, for Allah is wise in all His actions, and the lack of knowledge of wisdom does not mean its absence. Most scholars have disliked delving into divine decree (al-Qadar) because it is one of Allah's secrets. Belief in al-Qadar is obligatory, and researching it may lead to denying or objecting to it. The only way to know about al-Qadar is through revelation from the Qur'an and Sunnah, for al-Qadar is one of Allah's secrets that He has kept exclusively to Himself.