Discobabe - Please ignore the advice from FishWithABicycle. It contains numerous errors.
The fact they have one extra if anything slightly reduces your chances of getting a place. But if they are only one over many appeal panels would be happy to admit one or two more unless the classrooms are very small.
Buying a house in the area makes no difference to your appeal at all. It moves you up the waiting list but the appeal panel don't care about that. What matters is how good a case you can make. If you make a good enough case you can win an appeal for a school 50 miles away.
Your case must be about why your son needs to attend this school. Simply going to the same school as his sister or being a local school won't help. You need to show that this school offers him things that are missing from the allocated school (or his current school if the LA hasn't offered you an alternative) that are particularly relevant to him.
FishWithABicycle - I'm afraid the advice you have offered is very poor.
buying a house in the area won't hold any weight until you have physically moved
Wrong. For appeal purposes it won't hold any weight. Period.
Exchange of contracts doesn't count
For the purposes of the waiting list most LAs will accept exchange of contracts as confirming the new address and won't require further proof of the new address.
But after age 7 the class size is allowed to go up to 35
There is no limit on class size in Y3 and above. Most appeal panels are unwilling to go beyond 33 or 34 but a few will go higher.
you may find that once you have moved you might get a place
Whether or not Discobabe has moved is irrelevant to her appeal. And if there is a place available at the school it must be offered to her even if she lives hundreds of miles away.
There is absolutely no point in appealing unless they have made a mistake
Rubbish. This is for Y3/4. It is not an infant class size appeal. Discobabe can win by showing that the disadvantage to her son from not attending this school outweighs the disadvantage to the school from having to cope with an additional pupil. Appeals for Y3 and above are regularly won where there has been no mistake.