For your first question, as long as Tuition was paid, the school will send a 1098-T even if grants, scholarships or student loans were used to pay. In the past, it is possible that his tuition was paid with waivers, this type of payment is not reflected on 1098-T since a waiver waives the Fees as if they were never paid.
I would double-check your entries for Form 1098-T to make sure you entered Box 5 amount. If Box 5 amount wasn't entered, TurboTax will enter $3k as qualified school expenses paid, therefore qualifying you for the tax credit.
