Q. 1. Do children go to Hell. We never hear anything about this matter in the teachings of the Catholic Church?
A. 1. According to the Canon Law of the Catholic Church, "A minor before the completion of the seventh year is called an infant and is considered not responsible for oneself (non sui compos). With the completion of the seventh year, however, a minor is presumed to have the use of reason." [Catholic Code of Canon Law # 97 §2]
For the above reason, the Catholic Church teaches that a baptised child age 8 and over can sin.
If a baptised child does wrong prior to having reached the age of reason, that wrong is not considered a sin that is held against the child on Judgment Day. But, if a baptised child age 8 and over does commit mortal sins and dies without having confessed such sins, he faces eternal damnation unless the mercy of God, for unknown reasons, dictates otherwise.
"As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: "Let the children come to me, do not hinder them," [Mk 10 14; cf. 1 Tim 2:4] allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism." (Catechism of the Catholic Church # 1261)