Armybrat,
The AFA does state the mins on their admissions web page, however, they state it in a particular way. I.E. they say a 24 or lower on the V and 25M of the ACT
"normally will not be competitive for an appointment"....hint hint don't expect to be a candidate (those words are directly from their web). You always want to be above the mean whenever possible. For the AFA it is 1305 out of 1600 or a 30 composite for the ACT. For the SAT they state 580 V and 560 M
As far as the CFA you are correct no mins are ever stated, but the maxs are. It is important to get as close to the max, especially for the AFA because they recognize that due to the alt. cadets will score lower when they get there while adjusting to the alt. This is why they look for strong scores.
Realize that during the yr you will read that some kids are asked to re-take their CFA. The reason this occurs is because it is low and the candidate is viewed as being very competitive, except for this part. Don't rush it, get to the max and then hand it in. Before anyone asks, no you can not ask to re-take it only the SA can.
For the nom process you should also realize that the committees have been doing this for a long time, thus they know from history the SAT/ACT scores that are the median at the SA's. They are going to take a longer look at the whole candidate if the SAT is low. (are they poor test takers?) Conversely they will also look at the candidate a little deeper if they have a high SAT and low gpa (are they smart, but slackers) At DS's interview they looked at his transcript and saw 1 C (quarter grade period not final) it was in AP Calc. They asked why did you get a C? He explained that it was material that he did not "get" originally, but by mid-term he had a B. Be prepared to answer questions like that if you have a little ding on the transcript. If you can logically explain it, they will move on, if you don't they might continue with the questions. I.E. poor answer would be I hate Math!
It is not uncommon for 70+ candidates asking for 1 of the 10 noms. In areas like NoVa which is competitive it could be even higher.