Education

First question about your son's return:  Yes, your program gave you the taxable amount to use. The IRS will not be cross checking as your tax return does not show that amount, it is just a courtesy of the program.

To enter the taxable income from the 1099-Q, you will enter the one in his name and subtract out $xx qualified expenses to give you the correct taxable amount. The amount subtracted will be less than total expenses. It is just the variable needed for the correct taxation value. It looks like the 1098-T would also need to be entered.

Second response: 

Your AQEE of $2343 is 1098-T box1 minus box 5 plus the $18 other expenses. There is no consideration of the 1099-Q income which is either pure income with no credits, or it must be accounted for in your calculations.

You have Q income of $15,000 plus  1098-T scholarships of $8125 = $23,125 total income minus expenses of  tuition, supplies, room and board $10,450 - $17.55 - $4525 = $8,132.45 income to the student. 

You can shift more income to the student for you to claim education credit. I hope the room and board is for one semester rather than a year.  If AQHEE falls short of gross distributions, some portion of the earnings shown on Form 1099-Q will have to be reported on Form 1040 as ordinary income, and you or your beneficiary may have to pay an additional 10 percent penalty tax on the taxable earnings

Don't forget the kiddie tax. Please see another post of mine here for more details of the 529 exceeding college expenses. 

See 

What is the Kiddie Tax?, 

IRS Publication 970, Tax Benefits for Education 

@fanefamily5