Hell, Dave - big question!
Here - CAtholic schools are private schools. There's a Catholic primary school in most areas - and that's what your kids will need.
I'm not sure about following the UK curriculum - I wouldn't imagine it's be too different from what they teach here - but then, I'm a kid-free zone and a teacher-free zone - so don't really know.Turramurra is a nice area - but a fair way out of the city (in my opinion - and I lived there for a while) If I as going to live in Sydney for 4 years only, I'd like to be somewhere more active / involved. Turra is pretty staid / conservative / stuffy /monied! You may find this attractive in a suburb
Think about the eastern suburbs - still a good transport network, but more cosmopolitan, and beaches are close.
Or - inner weestern suburbs (where I live) good mix of people, variety of housing, good transport.
Have a look at domain.com.au - to see what sort of thing are available.
Ask any further questions here - I'll keep an eye on it. Unfortunately, I'm probably the only active Sydney member on the board right now - but I have lived here all my life (so far!)