Is it true that illness is of the same kind as sin, and that diseases of forgetfulness such as Alzheimer's and amnesia occur due to slandering people? And what are examples of other sins and their corresponding illnesses?

Recompense is of the same nature as the deed; this is a general principle indicated by the texts. Calamities and illnesses may be a punishment or a trial. However, to definitively state that a specific person's illness is a recompense for a particular sin is not correct; rather, it is speaking about Allah without knowledge, because its cause is unseen, and Allah has not informed us of it. It could be a trial or a punishment for another sin. Therefore, a Muslim believes that recompense is generally of the same nature as the deed, but it is not permissible for him to assert with certainty that a specific illness is a punishment for a specific sin, because that pertains to the matters of the unseen. Allah Almighty said: (And do not pursue that of which you have no knowledge), and this includes every statement made without knowledge or action done without knowledge.