I earned a small amount of exempt-interest dividends, some from nearly every state. Must I enter the state and the amount for every state or is that an option?

No.  You do not have to enter each state and the corresponding amount. After entering your 1099-INT, mark the button for "I earned tax-exempt interest in only one state."  From the drop down menu for state selection, scroll to the bottom and select "Multiple States".

I wasn't able to return to the point where I could test your answer.  TT had closed the questions and I couldn't find any way to reopen them, so I asked how that could be accomplished and am as yet (some four days) waiting for an answer.

Tax-exempt interest is interest income that is not subject to federal income tax.. The most common sources of tax-exempt interest come from municipal bonds or income-producing assets inside of Roth retirement accounts.

To revisit the interest section:

• Login to your account.
• Select Federal from the left menu
• Go to Wages and Income then Income and Expenses.
• Scroll down to Interest and Dividends.
• Select edit next to Interest on 1099-INT.
• Select edit next to the interest that you need to adjust