My question is: Is a child's prayer answered?

The response to supplication is a matter of the unseen. In this regard, a child is like an adult: their supplication may be answered or it may not. Some scholars hold the view that a child's supplication is more likely to be answered because they are free from sin. An example of this is the funeral prayer (Salat al-Janazah (definition)), where the supplication for the young deceased is considered more likely to be answered.