"However if a child plays sport for a school and gets injured what happens then."
Every school or intramural program I've ever encountered required liability waivers and the participant's own health coverage would deal with expenses due to sports injuries. Unless the school could be proven negligent in some way the school wouldn't pay.
"Some of the players look as if they come from homes that cannot afford insurance so does the school provide this for the team while they practise or play?"
The school wouldn't get involved but there are a number of public programs for health insurance that cover people who can't afford coverage.
"We do have government-sponsored health insurance in most states that will cover children in low-income families, but once you hit 19, it is much more difficult to qualify for those programs—which is unfortunate for college athletes."
Most college athletes can get reasonable health insurance through the school. Given that most college level athletes who can't afford their own coverage are there on grants or scholarships, it's often covered as part of the package. It'd be a rare college team that would allow an athlete to participate without coverage due to liability issues.