So sorry, frying things are a but mad atm. During the day I didn't really get the chance to reply properly, and come evening I was too tired to.
With my experience so far, I would dare predict that you would probably need your ds' dx confirmed by a German body. 2.5 yrs ago we moved from the North to the arhineand Palatinate region. Before I was able to get any sort of support for both myself as well as ds1, I had to have him seen again. At first I was told that we would have to go through the whole dx process again, but I old them that was reficulous, and added, very unnecessary stress for me and ds1. Especially considering his dx wasn't even 3 months old...
We had ds1 tested in Hamburg at the Autismus Institut and found them very good. In any case, as soon as you know are def moving, you could phone them, ask to speak to the director (not impossible, I did!) and you could ask for advice what to do next, where to turn to etc
TAs, as they exist in UK schools, don't really exist in German school. And German teachers seem to be very touchy about having another adult in their class room, I guess worried about being judged/assessed?? What your ds would be entitled to is a Integrationshefer or Schulbegleiter. The hours/week get approved and paid for by the Jugendamt. In order to get as many hours as possible approved from the start, come over wih a big paper trail. And if you can show he is already getting 1-2-1 atm, I am sure it would help a lot.
Other things you can apply for once you are here are Behindertenausweis ( which will be useful for e.g. Your tax return), pflegestufe (both ds1&2 have Pflegestufe1, which means I get Carter's allowance of €315/month/child, as well as a yearly budget of €1500/child that I can use for e.g. Babysitters or people helping me out around the house with the boys. We also get something called 'zusätzliche Betreuungsleistungen' which is a Budget of €200/Month for babysitters/carers. But for this one you can't choose your own but it has to go through a professional service.
Anyway, overall, once you know what's available and what you are entitled to, I find that there is loads available. And according to the professionals we see here, authorities in the North are even more generos than they are here.
We are a member of the local Behindertenhilfe. They were great advising me what my rights are etc. and they would also complete all the forms for applying for Ehindertenausweis, pflegestufe for you. And if something got rejected, they'd fight for it for you. Membership is something like 25€/year, and well worth it!
Right, loads (probably too much) of info here, but who knows when I will be able to post again 