Questions about Denmark (Copenhagen)

Hello,
Hopefully, this is the right place for this thread.
I am very actively considering moving to Denmark for a few years and see if that's a country we want to settle down in. I work in IT and am in mid 30s. The reason we want to move from Australia is that Denmark is one of the top countries to raise kids. My questions :
1) Is English widely spoken in Denmark/Copenhagen ? I understand I will need to learn Danish if we live long term.
2) Is Denmark really the best place to raise kids ?
3) Is healthcare free for residents ?
4) Is education (all the way to uni?) free for kids ?
5) Will I have to pay taxes in Australia on my income in Denmark ?

Cheers,