what happens to the net public debt if the federal government operates next year with a : budget deficit, balanced budget, budget surplus

Answer 1

The federal debt increases each year due to interest costs.
So, if there were a budget surplus GREATER than the interest costs, the debt will go down. Otherwise, the debt keeps increasing.

Some will argue this is wrong, one should only consider "real, non inflated" costs. I am not so certain that is much more than smoke and mirrors.