Since you didn't pay any foreign taxes, you can leave that section alone. Any foreign income that needs to be entered on your tax return should be included in the amounts entered on lines 1 to 11 on a Form 1065 schedule K-1. The only reason you might need to enter it is if you reported foreign taxes elsewhere on your tax return, in which case you could enter the foreign income where you apply for your foreign tax credit.
If you add income to your federal return, it may result in taxes due on your state return, but not necessarily, especially if the income was not earned in one of the states your filed for. If the state tax does not change, you don't need to submit an amended return for that state. You should prepare the state amendments though to see if the tax changed.
The supplemental information is used to determine how to handle entries on the schedule K-1, it is not normally additional income, deductions or credits that need to be added. So, if you see questions in TurboTax as you enter the schedule K-1 information, you can refer to the supplemental information for clarification.
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