No. You have described some reasons why his statement may not be usable against him, but there is no law forbidding the police from asking questions or even tricking a person, even if they are mentally ill or very low iq. It happens all the time.
His cognitive abilities would be a factor in determining whether he knowingly, voluntarily, and intelligently waived his right to remain silent or his right to an attorney, but the (likely) only remedy for a violation would be suppression of his statement at trial.
He needs a lawyer to discuss his history of mental illness and cognitive abilities to determine if they will provide a defense to the charge.