Q. Are my assumptions correct? No taxes.
A. Yes, in both cases.
I didn't re-do the math for son 1, as your revised numbers didn't change anything.*
For son 2, I don't see where your $28, 876 comes from. But, it doesn't matter.
$16,929 + 8008 + 1298 = 26235 - 2500 -4000 = 19,735. That results in about $42 of reportable income. Since he has no other income, he does not need to file. So, no tax (and no penalty since the scholarship/credit exception applies).
*Technically, you may not be able to use the $8,162 rent you paid. For off campus living you use the lesser of your actual cost or the school's "allowance for cost of attendance" (basically what on campus residents pay).
