Sorry, in answer to the second part of your question, SCOTUS is an appellate court only; it doesn’t hold trials exactly, it only looks at questions of law on appeal from lower courts (except in very rare cases). So they are really interested in the decision of the lower court and the questions of errors of law that are presented. Those are the only things taken up by SCOTUS, not the entire case top to bottom, so they may only look at a narrow issue. That’s what they were doing here.

So the information they would need from the lower court is minimal, and would be alleged by the party appealing the ruling of the lower court: what is it that you think that the court got wrong in applying the law in that case?