Q. 1. Does the Catholic Church anoint sick children when it anoints the sick?
A. 1. Your question appears to address two issues related to the anointing of the sick, first the anointing of the children and secondly the general anointing of the sick. First, let us see what the Code of Canon Law states on the matter of the anointing of the sick.
"THOSE ON WHOM THE ANOINTING OF THE SICK IS TO BE CONFERRED
Can. 1004 §1. The anointing of the sick can be administered to a member of the faithful who, having reached the use of reason, begins to be in danger due to sickness or old age.
§2. This sacrament can be repeated if the sick person, having recovered, again becomes gravely ill or if the condition becomes more grave during the same illness.
Can. 1005 This sacrament is to be administered in a case of doubt whether the sick person has attained the use of reason, is dangerously ill, or is dead.
Can. 1006 This sacrament is to be conferred on the sick who at least implicitly requested it when they were in control of their faculties.
Can. 1007 The anointing of the sick is not to be conferred upon those who persevere obstinately in manifest grave sin."
According to Canon Law # 1004 §1, the Sacrament of the Anointing of the Sick is to be administered to those who have reached the age of reason. What is the age of reason?
"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." [Canon Law # 97 §2]
For the above reason, the Catholic Church teaches that only a child age 8 and over can sin.
So can a priest administer the Sacrament of the Anointing of the Sick to a 5 or 6 years old child? If it can be shown, beyond any doubt, that the 5 or 6 years old child knows the difference between right and wrong, therefore making it possible that this child has sinned, than "Yes" the priest can administer the Sacrament of the Anointing of the Sick to this child. Otherwise, it cannot be done because the child under the age of eight is considered innocent and freed of sin from the Sacrament of Baptism.
Regarding the anointing of children when there is a "general anointing of the sick," such is not permitted, not only for the children, but also for the adults. The administering of "general anointing of the sick" is a liturgical abuse. The Sacrament of the Anointing of the Sick is not to be administered to groups who have a variety of ailments such as mental illness, migraines or kidney stones. This Sacrament is reserved for those who "begin to be in danger due to sickness or old age." That means they may die from their illness, maybe not right away. One should not wait until the person will die in the next 30 minutes. If it is obvious that the person is seriously ill, then this Sacrament should be immediately administered to that person.