My son is in reception and he's my second child so I've seen it all before.
Firstly - your Dd isn't behind because she can't read yet.
In ds's class here is one fluent reader, one self taught fluent reader (which means he can read really well but his unobservant parents didn't notice and so he doesn't know phonics such as "sh", "ch" and "th"), several who are blending the odd word and then a complete range down to a few who don't know any phonics or letters at all.
(Mine is the self taught fluent reader btw - which is how I know this as I've had conversations with his teacher about whether to group him with the fluent reader or the "blenders".)
They do start them off very slow with sounds. If it is the same as ds the. They will be doing "SATPIN" and they do spend a lot of time on each letter. Ds has been "blowing out a candle" (P) for days. But the reason is that once they get these down pat then there is a huge number of words that they can blend. So they will then be blending in groups as well as learning more phonics.
I do understand your concerns about free flow - I remember being very concerned about how Dd would learn to read and write - she was in a free flow of 90 - but she did! They all did! I have no idea how - they have no desks! - but friends also have kids in free flow reception and they all learnt to read and write over the year as well. It is like magic.
Re:- wanting to do learning when she gets home - that's fine - means she is enjoying learning whilst not realising. Some days ds wants to read and read when we get home, some days he wants me to read to him, some days he wants to plays games / toys, most days he wants to watch Thomas the Tank. I just go with it. (Although I do limit Thomas telly watching!)
Re:- violence in the classroom and the school not taking it seriously - that is an issue and I would be concerned about that. Have you been into school and tried to discuss just that with them. (If you turn up with a list and start talking about your dd's aspirations then the real issue -the violence - may get lost in the middle.) I would move my child if there was repeated instances of violence and no proper action taken by school.
However, as other people have said, don't expect perfect behaviour from a private school. Dd goes to tennis lessons and happens to be the only one of 8 there not from a particular local private school. The standard of behaviour from 2 or 3 of the others is really really bad. I was really shocked. (Not least because our current plan is to send Dd and ds to that school at 11!)