Thanks for your questions. I'll try to answer them as best as I can...
what age do children start school
Children here start school, in børnehaveklasse (I suppose you call it kindergarten in English), when they are 5-6 years old. They have to be enrolled in school in the year they turn 6.
when they start more formal learning are there still opportunities for play?
Absolutely. There's a lot of room for creativity, play, physical activity and discussions in Danish schools. In many ways, pupils have a say in their own education as they get to choose topics they would like to research and write projects about. And project work in Danish schools almost always require an element of creativity. As far as I know, pupils have to spend part of their lunch break playing outside.
How many times a week do children do sport?
I believe P.E is on their schedule once a week, and it's a mandatory subject from 1st grade until pupils graduate in 9th grade.
How long are school days
The younger kids are typically in school from 8.00 to 14.00, and the older kids are in school from 8.00 to 14.30 or 15.00.
do children take lunches in or do they eat at school?
Kids typically bring their own lunches from home, but some schools have small cafeterias where the kids can buy things like sandwiches, salads, fruits, etc. Some school even sell hot meals like spaghetti bolognese, rice with curry, etc.
I wonder if its an issue in other countries to or if the education system is so different that children are happier and needs are better met?
There's definitely an increased problem with anxiety amongst children here, sadly. There's a lot of awareness around this issue, and efforts are made to accommodate children with special needs. But there's still a lot of work to be done to help children who need support.