Federal Judges are appointed by the president. The senate needs to also confirm the appointee.
A Majority Opinion is important because it shows how similar cases in the future will be held
The current members of the Supreme Court are:
Clarence Thomas, Ruth Bader Ginsburg, Stephen Breyer, John Roberts, Samuel Alito, Sonia Sotomayor, Elena Kagan, Neil Gorsuch, Brett Kavanaugh
The supreme court deals with cases that are forwarded by the lower courts. they also deal with overseas lawsuits.
Hope this helps!