1) Do schools ever (particularly in these cash-strapped days) want the applicant so much (because they agree they would be a great fit and a good student) that they will agree to take them regardless of the views of the rest of the appeal panel? (ie if the panel thinks their arguments are weak but the school likes them)
I don't think so, if this is the normal point of entry, and there are other appeals taking place
If it were to happen, it would be entirely outside
the appeal process, and there would have to be a legal justification - a temporary increase in the PAN, for example, sufficient for the child to be given a place under the admission criteria. (The school cannot pick and choose which particular child it wants.)
However, in the case of a single (probably in-year) appeal, it wouldn't be difficult for the school either to hint that it would be happy to take the appellant, or alternatively to offer little resistance!
2) Does the panel know where they have an offer? For example if School A is perfect but school B could meet most of their needs (at least on paper) but schools C-F would not, if they were offered School B would the panel be aware and say "but you have B so you don't need A". If that were the case would they be aware if the parents turned down B in the hope (possibly extremely risky hope) that the appeal panel would say C etc do not meet the needs and therefore agree that A would be better.
What the panel know about preferences (and offers) varies!http://www.elevenplusexams.co.uk/appeals/general#a21