To answer your questions, working backwards:
No, a candidate can be triple qualified and still not receive an appointment. Triple qualification is just a final screen to narrow the pool.
Nobody "determines" if a slot will be filled as it depends on the nomination process of the congressman. If it is the Principal-and-Numbered Alternate process, then, yes, both slots will be filled assuming the congressman submits 2 separate lists. If he/she submits only one, chances are only one will be filled. If it is a Principal-and-Competitive-Alternates and the Principal candidate turns down an offered appointment, then there is no guarantee that the Academy will go back to the list to offer the appointment (this is a real sore spot with a lot of people). Legally, the Academy MAY or MAY NOT go back to the list---no guidance is offered as to what they should do. If the process is the Competitive Alternate list, the same situation applies.
My thought is the Congressman should have plenty of push to have his/her slots filled by the Academy but different Congressmen have differing interests with regards to the Service Academies. A phone call from the Congressman's office to the Admissions Office expressing a strong desire to have the two slots filled that year by a couple of the fine qualified candidates in the lists submitted SHOULD swing some weight, to my thinking. In fairness to the Congressional offices, the actual charging of the appointments is done at the very end of the cycle and busy congressional staffs often miss just exactly who got charged to whom unless they are focused on it. They may THINK that their two slots are going to be filled but find out differently much later after the class has been filled.