Not if you aren't 3Q. His math score is on the cusp of being academically qualified/not qualified for the academy, but may be a good candidate for prep because he is strong in all other areas. But you just never know what can happen. He has a solid plan either way so we aren't as stressed out anymore waiting.
No. Even if you are 3Q and have a principal nomination, you can get a TWE.
The only thing that makes an Offer of Appointment "automatic" - is a Letter Of Assurance - as long as you satisfy the condition(s) of the LOA.
The wait is of course... agonizing. I know in the end it is all going to be fine, and we will all have good lives regardless of the outcome here. In the meantime, I think I need therapy.