1 The Headmaster of his current school is not aware of the appeal and I am not sure if he can contribute to appeal process. Will that be a negative for him? I could request for a letter from the Head, but it wouldn't be the same as other Heads who know the process.
The Head needs to write about your son's ability and his suitability for a grammar school education. It shouldn't really matter that he doesn't know the system in Bucks.
2 He has no medical problems, so no letter from the GP, would that pose a problem?
It is by no means the case that every appeal rests on medical evidence! Your mitigating circumstances are the proximity of the school exams, the travelling, etc.
3 He is quite good in Sports too and is on the School Football team. Is also good in Squash and has played on the School Rugby & Cricket teams too. Would mentioning this help?
4 Lastly, would it be possible to request for an appeal before the start of the Holiday season.
It is very hard to tell when your appeal might happen, but I suggest that you call the Appeals department to ask. Obviously they can't schedule the date until you have submitted your form though.