I'm hoping to get some advice about relocating as a family from the UK to Vienna. I am Austrian on paper, but moved the UK when I finished school aged 18 for a gap year, which has now lasted many, many years

We live in the South East of England, which -unfortunately!- is one of the most expensive areas in the country, and are struggling more and more with the very high and ever increasing cost of living, lack of family support, long distances to visit elderly relatives, the overcrowded and underfunded school system etc. After some very successful visits and stays with family back in Austria over the years, we are now thinking of moving back in time for my oldest to start school in September 2020. I was never an adult in Austria as I moved to the UK straight from living with my parents until I finished school, and never had a job there, so this is all very new to me.
Our plan is along the following lines: my husband will take a CELTA certificate this summerand try to find work teaching English in Vienna. He doesn't have a university degree which unfortunately means he probably won't be able to apply for a teaching role at an Austrian school, as far as I understand it. Has anyone here got experience of how easy/impossible it is to find work teaching English as a native speaker? His German is basic but functional.
I have a PhD offer from a UK university which will start this September, and can be done remotely (also from a different country). I do not know how health insurance would work if we moved to Austria with my husband looking for work, and me receiving a scholarship from a UK university. Does anyone what criteria there are for Krankenversicherung, or who I can contact to find out about how to set up health insurance?
We will move with our children, aged 5, 3 and 6 months. I have come across VBS bilingual primary (English/German) schools which seem perfect but oversubscribed. I am completely unfamiliar with the Austrian primary school application system - is it possible to apply for a bilingual school place before being a Vienna resident? Is catchment area a criteria like it is here in the UK?
Finally, I am confused by how much financial support we may be eligible for, I believe there is FAmilienbehilfe, and possibly Kindergeld as well, which we may be able to claim. Can this be set up after moving to Vienna, and is it linked to us being in work already? I am also looking into Wohnbeihilfe as our income is likely to be quite low in the beginning, but again, am finding it all a bit unclear. Does anyone know who is best to contact to find out more info about this?
sorry for all the questions, I am at the very beginning of this journey, and would hugely appreciate any advice you can give me. Would also love to hear of anyone who has made this move already, and their experiences of adjusting to Austrian family life.
Many thanks!