Should the government intervene in medical cases for minors, and under what authority?

Absolutely not. Allowing religious wing nuts to pray for healing of lethal disease rather than relying on science is the only way to improve the gene pool short of calling for Holy War against Islam and giving them all a rifle and a one-way ticket to Afghanistan.

Yes I think that every american in this country should be cover as is every member in congress through a government health care plan if they chose to do so .

Intervene under what circumstances?

The government already provides health coverage for children and senior citizens.

Yes, when the parents are jeopardizing their child's life through delinquency or superstitious beliefs.

That child is not yet emancipated and relies upon his parent's for proper care. I hope that kid survives and that the parents are thrown behind bars.