The notes look quite good on the whole. With individual stage ones, it doesn't surprise me that something that wasn't said finishes up in the notes!
A couple of points that you raised might have been omitted, but the notes are not required to be verbatim, so this is probably acceptable provided that the points were not crucial. (Even so, it would be difficult to prove the omission!)
The panel's deliberations show that they concluded that your daughter is
of the required academic standard. They appear to have decided that the school had not entirely made its case (this is sometimes called 'part prejudice'), and that another 8 children could be admitted without prejudice. They compared cases with a view to upholding those that were strongest in accordance with 3.9 of the Code. (Having read your presentation, I happen to think that you put forward a very good case. What we don't know is just how compelling the other cases were - and I'm afraid you're unlikely to get any explanation why your case was not one of the strongest, as this is a largely subjective judgement on the part of the panel, and, as I mentioned before, there are data protection issues in relation to the other children.)
I wouldn't want to raise your hopes, but I think you should ask the EFA to clarify the panel's decision-making process for the following reason:
1. If the panel decided that 8 children could be admitted without prejudice, then they are required to allow at least that number of appeals.
If they decided that your case was not one of the 8 strongest - a judgement that we cannot challenge - they should then have gone on to consider whether or not your case outweighed the prejudice to the school. The decision letter states "The panel did not accept that your case was sufficiently compelling to outweigh [the prejudice]" - but the clerk's notes do not say this (they refer to a comparison with other cases).
2. The clerk's notes include the statement that there were "several cases which merited admission .......... but the school could not cope with that number of successful appeals" - but this comes before the decision that an additional 8 pupils could be admitted without prejudice!
3. Either the case failed because it did not outweigh the prejudice to the school - or it did outweigh the prejudice, but the panel judged the school could not cope with that number of successful appeals. It cannot be both, and it is surely not acceptable to have a decision letter that is at variance with the clerk's notes of how the panel arrived at their decision?