Yes, those are the right questions.
If the school now changes its story the appeal panel should look very closely at that to determine what has really happened. They certainly should not just accept a bland statement from the school that they got the letter wrong. The council may not know one way or the other but there is nothing to stop you asking.
The school is permitted to limit the number of places offered in various categories to a degree but, if they do, this must be clearly stated in their admission criteria. It does not sound like this was the case.
The child with a statement of SEN will have been admitted automatically. Such children do not go through the normal admissions process so what category they are in is irrelevant. If the admission number is 42 they should not have offered 48 places unless the LA has agreed to a variation of the admission number. If they can admit 48 why not 49 or 50? Or have they admitted 6 children as a result of mistakes? An admission number of 42 or 48 would not normally be infant class size but that doesn't really matter in this case as it sounds like you have clear evidence of a mistake. The school will say they cannot accept any more children. That is always what they will argue at any appeal. That won't stop the appeal panel admitting your child if they think you have a good enough case.
The waiting list has to be in place until Christmas. It is up to the school whether they continue to operate it after that. You could ask them but it isn't relevant to your appeal.
The school must conform to its current published admission criteria. They cannot give someone sibling priority on the basis that the criteria were different a few years ago. They cannot apply any rules other than those stated in their published criteria.
Council involvement is no guarantee that waiting lists will be operated correctly! The school must tell you how long the waiting list will be in place. Some schools and LAs are reluctant to tell people their position on the waiting list as many parents don't understand they can go down the waiting list as well as up. There may have been other factors of which you are not aware that gave the children priority for nursery but equally it could be that the waiting list was no longer in operation and the parents happened to apply when there was a place available. If another child is admitted off the waiting list when you believe yours should have been you can appeal.
If any parents reject a place it must be offered immediately to whoever is top of the waiting list. They cannot sit on the place until September. However, if they have admitted over PAN there won't be any vacancies until the number of children drops below 42.
Your second point isn't particularly strong. By far your strongest point is that the school has not complied with its own admission arrangements.
SchoolsNightmare is right that, if a mistake has been made, they should admit your son without an appeal but most LAs and schools (and it is the school that makes the decisions in this case) insist on an appeal.
If you would like me to check the admission arrangements to make sure you haven't missed anything let me know which school and LA we are talking about. Feel free to PM me if you don't want to post this publicly.