The deadline is for the LEA's convenience in setting up and managing the appeal panels. They can't refuse to hear your appeal just because you submit your appeal (or supporting documents) late. The panel will see everything you submit. Probably the best thing is to give the outline of your appeal on the initial form - this need not be anything more than a list of bullet points, eg limited choice of GCSEs/lack of provision for x and y/not equipped to meet child's particular need for z etc etc - and then say that you will expand on this in a later statement and/or your comments to the panel. Don't, though, submit documents very late - or produce a wodge of new documents on the day - because the panel may have to adjourn to consider them, and a delay doesn't help you.
If the school is an academy then presumably it is its own admissions authority and will be arranging its own appeals (although some academies buy in the services of the LEA to do this). In any event, the school should be providing you (within reason) with any information you need to prepare your appeal.
The letter telling you that you had not got a place should have told you the reason for that. This is crucial and you must press the school/LEA, as how else can you check that the decision has been correctly made, eg distance from home to school has been measured correctly and/or your child has been placed in the right admissions category?
Do not accept their lack of help on either of these points. You could drop it into conversation that if they obstruct you in preparing your appeal and refuse reasonable requests for information you will be using that as further grounds for appeal and/or formal complaint. If, for example, they won't confirm why you were refused a place, then (in your shoes) I would be saying to the panel something on the lines of "as the school/LEA won't confirm that my child's application was dealt with in accordance with the admissions code and the school's admissions criteria, I have to assume that some mistake was made that deprived my child of a place and this is a cover-up". That on its own isn't going to win an appeal, but it puts the onus on the LEA to convince the panel that the application was properly and fairly considered and may lead the panel towards giving you the benefit of any doubt.