Room and board and computers are qualified expenses for a 529 plan. If the student lives at home, you can use your actual food cost or the school's meal allowance. In your case, prorate it for the 1 month.
Come up with a room & board amount and then let's allocate the numbers.
Are you saying, for sure, that the $2000 scholarship was required to be applied to tuition?
Your accounting is basically correct, except that it does not contain amounts for room and board.
