If child is eligible following panel decision and meets criteria in terms of postcode then should we not be offered a place
Yes, but don't forget that they are not just looking at your appeal - they're looking at all the appeals that they have decided are eligible and balancing them against the school. In a simple case - they found that there were two appeals eligible, and then decided that the school could only accommodate one more pupil without damaging all the other pupils - then they have to decide which one to allow.
or at the very very least added to waiting list,
Down to the school now - appeals are totally separate to the waiting list. Unfortunately if they've allowed more appeals, then the school will be oversubscribed and they won't be able to allow anyone else off the waiting list until it's back down to the published admission number.
Has panel been at fault by not asking what school we would send child to if not admitted?
No. In our area, the panels are supplied with details of which schools they have applied for and which one they have been allocated. We don't take any notice of the order they have put the schools down in - so you could have put the school you're appealing for as last choice, but we will treat the appeal equally to one where it's the first choice.
Letter says result is binding on school and panel- can we take further and to whom?
That's why it's an independent appeal panel - our decision is binding on both the parents and the school (so the school can't go off and say 'we don't want 8 more pupils - we're not having them').
If the process of the appeal was wrong you can take it to the Ombudsman, but not if you just don't like the decision the panel came to.
Only once has an appeal I was on a panel for been referred to the Ombudsman, and that was purely because the parents didn't like our decision - hence the Ombudsman rejected their complaint after investigating. More and more parents take this route now - they don't like the panels decision so think "we'll take it to the boss" - all the Ombudsman can do is order a re-appeal with a new panel, and of course, by that time the school is even more likely to be full to the seams so is less likely to succeed. But the threat of having an appeal go to the Ombudsman does keep us on our toes and both us and our clerks do our level best to assure that appeals are properly and fairly heard.