Are we sinful for not mentioning the deceased brother's children in the legal inheritance distribution and for affirming a testimony that he has no children, even though the purpose is to facilitate the inheritance inventory procedures and not to deprive them of it? And are they eligible for inheritance despite the difference in religion and age?

We have previously clarified the ruling on the inheritance of a brother's children. False testimony that the deceased has no children is a lie, because perjury is describing something contrary to its true nature. It is forbidden, even if intended to achieve a right. Your duty was to testify truthfully, and the court would have considered the disbelief or Islam of your brother's children. Fear Allah and repent to Him for this testimony by returning to the court and informing them of the truth about the existence of other children.