The rules are that appeals for on-time applications for secondary school (i.e. those relating to decisions sent on national offer day) must be heard by 6 July or the next working day, if 6 July falls on a weekend.
I agree with your son about not using a solicitor. It really won't help unless there is some obscure legal argument to be debated. My experience was that the presence of a solicitor or barrister altered the atmosphere of the hearing. It became more formal, more businesslike. I don't believe a panel would be prejudiced against the appellant who is legally represented, but there will be a subtle effect on the interaction between appellant and panel, and I suspect it might be harder for the appellant to gain the sympathy of the panel.
See also the Q&As, A11.
http://www.elevenplusexams.co.uk/11plus ... nswers.php