How is the concept of children being afflicted with diseases and disabilities to be corrected, and what is their fate in the Hereafter?

Allah tests His servants with ease and hardship for great wisdoms, among them testing their patience and gratitude, and so that people may know His power and wisdom. As for children, even though they are not sinful, their affliction is for a profound wisdom, among them testing their fathers and mothers, and to demonstrate Allah's power over all things. As for their destiny in the Hereafter, the children of Muslims will be in Paradise with their families, by the consensus of the Ahl al-Sunnah (definition) wal-Jama'ah (Sunni Muslims). As for the children of disbelievers, Allah knows best what they would have done. The correct view is that they will be tested on the Day of Judgment; whoever obeys will enter Paradise, and whoever disobeys will enter Hellfire. This is the correct position because Allah does not punish except after sending a messenger.