Hi there,
We have applied in parallel for our son's citizenship and then passport which were both processed within 4 weeks.
I think we have mentioned this in a separate cover letter we've written.
No, medical clearance and police checks were not submitted along with the initial application. I spoke to their customer service on the phone several times and every time I was advised to send in what we had to start the process.
It was a good advise, because our case officer came back to me and asked to NOT undergo health checks before 7th August. This is due their processing time apparently.
However I don't think it makes a difference, as health check results are valid for 12 months.
Police checks:
Because I've lived in four different countries within the last 10 years due to my career, it took a while for me to gather all police clearances (and it's very expensive).
If you have lived in the same country within the last 10 years, then it should be fine and you can just go ahead to request your police clearance. The UK one is quite expensive - £48 currently.
No guarantee for faster processing times with children, but: if you have children who are Australian citizens and are married, there is a good chance that you might be granted the permanent visa immediately or at least within 2 years. The temporary visa might be waived! I got this confirmed by my case officer
It's even written on their FAQ website, just can't find the link right now.
I just think I will do the health check here in London anyway, but will check first how much it would cost to do this in Australia.
We need to travel to Australia in 2 weeks ... (I will hopefully receive my tourist visa 676 which we have lodged separately).
Hope this helps a bit? Good luck with your application!