1. A person always reports wages earned on a tax return in their own name, never on a parents' return. Sometimes, if the child's only income is passive investments, the income might be reported on a parent's return.
2. Whether a child is required to file a return depends on the amount of earned and unearned (passive, investment) income. The rules are covered in publication 501. https://www.irs.gov/forms-pubs/about-publication-501
3. If a child earns money and files a tax return, that does not automatically disqualify them from also being someone's dependent. You have to look at the totality of their situation. See publication 501.
4. If a child claims "EXEMPT" on their W-4, this has NO EFFECT on whether or not they owe tax. Claiming exempt does not make them exempt. A person should only claim exempt--which blocks tax withholding--if they reasonably believe they will owe no income tax for the year. If they earn enough so that they owe tax, they must file a return and pay the tax.
