At open days you cannot be sure of asking a question about finance without others listening to what you are asking. Why ask about money and charges when you can do it privately? You could possibly find out before you go so if you cannot afford it, don’t go round the school.
Our school had an extras price list and it was readily available. Also if this is the only local private school, there might not be a huge choice! For most people, the cost of extras is not a major consideration. We don’t always know what DC will want to do and would you not go to an otherwise perfect school due to the extras costs? Most people know what the fees and charges are and make decisions accordingly.
I don’t recognise battered old Fords either. Never at DDs school! Not the Bentleys much either but talking to other parents can give you a feel for who is going to the school. Having been to several of these events over the years, there really is a difference in parents at different schools. Some posh schools have the parents to match. I never would assume a state school child, or new to private child, not fit in anywhere. Quite a few go private from state near me.
If you want a posh school, go for it. If you are looking at a GDST school then expect a wider variety of parents. I expected my DD to fit in. I didn’t want to assume she wouldn’t but I have no idea how you can really ask about this. If you think a school isn’t for you, then it isn’t, but DC is unlikely to get special attention because they came from a state school.
I wouldn’t worry about co Ed or single sex. If ss the best fit, so be it. My DDs went to single sex. They do meet boys! They are normal young ladies! They were not subject to anxiety or bitchiness. In fact totally the opposite. The girls were supportive of each other and both have hugely string ties with school friends beyond university. I would choose a school based on what it can do for your DD, not possibilities and fears that may never happen.