Ok.
So to summarise:at his previous school he was happy (ish)
There were behavioural issues not all of which were shared with you
At some point he has had assessments done which have suggested adhd
He mostly refuses to comply in the classroom and won't do work
At the new school he had a 1:1 from the first day. His behaviour was initially good (for him) but has been deteriorating.
He now runs and hides in school
You don't like:
The fact the 1:1 isn't the same person
The fact that the 1:1 is with him at breaks and lunch.
The SEN system in England is very complicated and it does sound a bit like you have got lost in it.
In order to get a diagnosis of either ASD or ADHD you need to go via a GP for referral and waits are long. School assessments can suggest or point to adhd or ASD but cannot diagnose. Given your son's behaviour I would strongly advise you to seek a referral from your GP for assessment for both ASD and AdHd.
Schools are expected to and do provide support without a diagnosis (not least because diagnoses take so long). His previous school has obviously taken advice on his behaviour and what might be behind it in order to help him in school,
They don't have to (and didn't) share every incident with you.
At the new school, there are a number of ways to fund support for children with SEN. The long term secure way is with an EHCP. Do you know if the school have applied for an EHCP?
In most schools, because the EHCP process is so slow, there will be a pot of additional money they can apply for from the council to cover the costs of the support while waiting for an EHCP. Used to be called emergency transitional funding or similar.
Again, school don't have to tell you where the funding for his 1:1 is coming from - some schools will fund it themselves out of budget. They should tell you when/if he gets the EHCP though.
Once funding is secured, it is considered best practice for the child to meet the 1:1 and it is also considered best practice for the job to split between at least two people. This means that the child can build a relationship with both people and the situation where he has built a relationship with Mrs X and then she goes off sick and he is extremely distressed doesn't happen.
However, at the moment most schools are really struggling to recruit TAs (largely because you get better pay on the checkout at Asda and nobody assaults you there) so there are children who have funded 1:1s who do not have a TA because the money is there but the school can't get anyone to apply.
Your child has a 1:1. It isn't ideal that the person who it is is changing but that may well be the best the school can do. You can say to the school that you would prefer it to be a regular group of two or three people but if they don't have anyone specifically for the job then there is very little you or the school can do.
When you say that the 1:1 is always there - this is known in the education world as a Velcro ta. It's not best practice, as ideally the 1:1 is able to help your child develop some independence.
Again, you can speak to the school and ask for the 1:1 to give him a bit more space, especially at break and lunch.
However be aware that this is a request, and if school feel he needs someone right next to him for safety reasons (eg he is a runner and they are worried he will jump the playground fence and get out into traffic) they don't have to listen to your request.
Their job is to keep him safe in school and ideally make sure he learns something. If you ask for things that mean he isn't safe they will say no.