What is the sin of children and animals that are afflicted by calamities, and is God's tormenting of all His creation without sin considered just, and what is the definition of injustice from which God is transcendent in this context?

The torment of some disobedient monotheists in Hellfire is not injustice; rather, "If Allah were to torment the inhabitants of His heavens and the inhabitants of His earth, He would torment them, and He would not be unjust to them." The hadith "The right of the servants upon Allah is that He does not torment them" does not contradict some monotheists entering Hellfire due to their sins, because they did not worship Allah as He truly deserves to be worshipped. Some scholars interpreted the hadith as referring to eternal torment in Hellfire, and that a monotheist will not abide eternally therein. Others hold the view that not being tormented applies to those who worshipped Allah and associated nothing with Him, and what is meant by worship is performing acts of obedience and avoiding sins, along with affirmation and belief. Scholars have mentioned other ways of reconciling, such as that not being tormented applies to those who are sincere, and that sincerity necessitates the heart’s realization of the meaning of the testimony. Another way of reconciling is that the entry of some disobedient believers into Hellfire is not torment but for their purification. As for the questioner's statement "I seek your aid then Allah's," the correct phrasing is "I seek Allah's aid then yours," because a Muslim does not put anyone before Allah in their requests, and seeking help from a creature in matters they are capable of is permissible.