You have many skeins of tangled thought going on in your pile of questions.
Let’s start with the last paragraph.
Realistically, it is quite possible to have an LOA and not be offered an appointment, because you don’t have a nom or are not fully qualified or don’t meet a condition stated in the LOA. It is also possible to have a nom for an academy and not be offered an appointment, even if fully qualified. Hundreds of applicants every year are fully qualified with noms, and there is not enough room in the class to offer them all appointments. It is all also true most cadets and midshipmen at service academies did not receive an LOA.
This is why you are always advised to have a set of non-SA alternate plans, such as college ROTC. There are many college and prep school re-applicants in each class. AROTC, NROTC and AFROTC are also sources of noms.
Now, noms. I’ve provided a link below that helps you see all the sources and numbers for noms. There are ones you apply for and ones the SA controls.
For the Senators and Representative, they can have 5 appointees charged to each of them at any one time at each SA. This usually means there is one appointee in each class whose appointment is charged to, say, the Rep, and 1 class with 2, for a total of 5 spread over 4 classes. Much depends on how many appointees graduated last May, because that will determine how many “slots” of the 5 are open in the next cycle.
Using our Rep, he or she can submit a slate (list) of up to 10 names for a slot, using a variety of methods to rank or not rank. They are free to use whatever process they wish in selecting their nominees. They are also free to collaborate with other elected officials in the state and do things like agree to not duplicate names across slates or only give 1 nom, regardless if the candidate has applied to 4 SAs.
One of the fully qualified applicants on the slate will be offered the appointment that is eventually “charged” to the Rep. You may hear that referred to as “winning the slate.”
Here is the key to understanding the “pool” concept: the SA can shop through any other fully qualified nominees on that slate and offer them an appointment, charging those appointments to nom authorities they manage. Those appointments are not charged to the Rep, though for publicity purposes, elected officials tend to gather up all appointees in their Distruct, regardless of nom source for press release purposes.
I believe USMA tells candidates if they are fully qualified (CFA, DoDMERB/medical, academic/scholastic). You might hear this called “triple qualified” or 3Q. I do not believe USNA and USAFA do so.
The SAs encourage you to apply for every nom for which you are eligible. Though you only technically need 1, if they wish to offer you an appointment, they have more flexibility as to where to charge the appointment.
There is much you cannot control about all of this. Put forth your best effort, be sure you have alternate plans and go PT when the stress gets to you.
Lastly, you may not hear about an appointment until well into April. Go look at the appointment list thread for the Class of 2026. You’ll see the bell curve of appointment deliveries.