Question 1: We cannot see your account or return, but what you describe sounds like you are entering the grant correctly. It is correct that the grant would end up providing taxability to your son's return. As a dependent filing taxes, his standard deduction is not $12550, but rather his earned income +$350, up to a maximum of $12550. Since the grant is more than $350 and is considered unearned income, the grant will produce (based on your numbers) about $550 of taxable income, which is likely $55-ish of refund reduction.
Question 2: See this website for Ohio filing requirements: Who Must File - Ohio Department of Taxation. There is a workaround you can try in case you are unsure. Your son can set up a TurboTax Online account, and you can prepare the return up to the point of clearing all the diagnostics. As long as you do not register the product, you will not need to pay for that preparation. But this will let you know if your son has a tax liability in Ohio or not. If he does not, then you can use the option on the website link above to file the IT-10 form instead of the full tax return. While this is prepared outside of TurboTax, there is no charge involved.
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