Yes, the student would file a Federal Return to get the federal taxes withheld back as a refund and select "Someone else can/will claim me" since he is a dependent on your return.
The student would be considered a resident of Illinois (since he is your dependent) and MAY need to file an Illinois return, depending on his income and exemption allowance. If he does not owe Illinois tax, and is only filing a federal return to get his tax refunded, he would not need to file a state tax return.
A 1099-G could report several different things:
If it is for a state refund and the student did not itemize on his 2018 Federal return (which he wouldn't have if he was a dependent) the state refund is not taxable and is not reported on his 2019 tax return(s).
If it is for unemployment or other income, it most likely does need to be reported on his return.
The 1098-T is entered in your Turbotax program and used on your return if it allows you to get an education credit. If it causes taxable income to be reported, the taxable income is reported on the student's return and your TurboTax program would tell you how much the student needs to report and how to enter it into his TurboTax program.
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