Does "Federal tax due" mean I owe the government, or does it mean they owe me?
Federal tax due near the top of your screen means you owe that amount to the IRS. Same goes with state taxes, e.g. NY tax due would mean you owe taxes to the state of New York.
If you're still working on your return, those numbers will likely change as you enter more items. Your tax due amount may even be replaced by a tax refund by the time you finish doing your taxes.