TurboTax definitely does support the Illinois property tax credit. I just checked and it's working fine in my software. What error message are you seeing when you try to claim the credit?
Here is information and qualifications for the Illinois Property Tax Credit.
Illinois does have an exemption from income for interest on US Government obligations. As long as you entered your interest on your 1099-INTs properly and noted the US government portions where indicated then that will carry over to the Illinois return.
Here is information on income exempt from Illinois taxes.
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