If God does not hear the prayers of unsaved due to the barrier of sin, is it then wise to teach unsaved children to bring their requests to God? I can understand teaching them to praise and give thanks, as even creation praises God i.e. declares His glory.
This is a difficult question, because the answer depends on the situation. Biblically speaking, God does not hear (meaning consider) the prayers of those who are not in Christ, for it is only through Christ that we may approach the Father:
Without Christ as High Priest, a person has no means of approaching God. God is only approachable by means of an intercessor, and the unbeliever simply has no intercessor before God. Therefore, instructing unbelieving children to pray is not a fruitful for them.
On the other hand, we cannot know the state of a child’s heart perfectly, and so we may inadvertently wound the conscience of a young believer by discouraging their prayers because we assume (wrongly) they are not believing in Jesus Christ. A child may, in fact, possess saving faith yet be unable or unwilling to express it to an adult, especially if that adult is not a parent.
Therefore, we cannot give you a single rule to follow under all circumstances, though in general we do not advise giving sweeping calls to unbelievers to pray to God. Instead, give them a presentation of the Gospel so that they might come to faith. Take note of Paul’s model in the book of Acts, where he frequently presents the Gospel but never instructs a crowd of unbelievers to pray to God.