Yes, your child can contribute $5,000 to a Roth IRA since she had taxable compensation of $5,000. No, for a Roth contribution she doesn't have to report the contribution. Therefore, she won't need to amend her return this year. But generally it is a good idea to report Roth IRA contributions. Later when she isn't a full-time student it would be important to enter Roth contributions to qualify for the Savers Credit.
No, a Roth conversion is when you contribute to a traditional IRA and then transfer it to a Roth IRA. Roth conversions are taxable unless you made nondeductible contributions to the traditional IRA (reported on Form 8606). The Roth contribution is the best option since your child won't benefit from a traditional IRA deduction with her low income.
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