my question is the letter from the Head doesn't mention his current reading age. However his last school report does say He has improved his (already high) reading age by 3 years, which is excellent! Will this report be sufficient evidence?
In my view, yes. (Draw the panel's attention to that line in the report.)
Also one of my reasons for wanting that specific school is he has a sibling who already attends. Do I need to put the reasons why that makes a difference on the appeal form or can I just say at the hearing?
Sibling should be mentioned on the form, but you could leave why it makes a difference until the hearing. (Most parents in fact probably don't elaborate, in which case it would be assumed that the usual sort of reasons apply - e.g. logistics, familiarity with the school.)