What is the ruling on buying nail polish for a young girl, and is fulfilling all of a child's desires to avoid suppression a sound educational approach?

If the objection to buying nail polish for a young girl stems from a belief in its prohibition, then this is a good inclination. However, there is no harm in using polish if it is free from harm and impure substances. As for fulfilling children's desires, the correct approach is to raise the child upon sound عقيدة (creed) and noble morals, and to develop their emotions and abilities while considering their health. The mother is responsible for this, and she must be wary of the widespread temptations.