I think you're thinking too much about it @busySunflower . It isn't as granular as you are making it. The panel has to make an overall assessment of whether your case for admission outweighs any prejudice to the school, and then if there are more cases that succeed in this than the school could take without creating a serious prejudice, which cases are strongest.
Some panels will want the parents to present oral evidence. In my LA the chair tended to say: "Is there anything that you'd like to add to your written evidence, that we have read carefully?" A parent is completely within their rights to read out their case, to read out a summary statement, or to simply say 'No'. It has no influence on the panel.
The panel will be deciding whether the school has established that they would be prejudiced by taking any other child, then, if they wouldn't, how many other children they could reasonably take, then (if that number is lower than the number of potentially successful appellants) which appellants have the strongest case.
In your case, they will be looking at whether being a young carer means that this school in particular is necessary for your child, and whether they will suffer prejudice by being denied a place.
All schools should provide support for young carers but if you have evidence that this one is particularly good, and perhaps evidence of why your child needs particularly good support, that will strengthen your case.