I don;t believe you can recess appoint a Supreme Court Justice. And I think it would be disasterous to try, even if it were borderline legal. I think all eight of the Justices would refuse to accept any such appointment.
George Washington appointed John Rutledge as Chief Justice by recess appointment. Justices Warren and Brennan were initially recess appointments of President Eisenhower.
Yes, you can.
The problem is that recess appointments are temporary, until the end of the next Senate session. They are not lifetime appointments.
If a Demoncrat President ever happens again, he would automatically get a Supreme Court nomination at that time. Such a recess appointment would be a highly unproductive use of an opportunity to select a Supreme Court Justice.
The same problem is of lesser concern for a cabinet post or any other appointment of one who serves at the pleasure of the President. A new President can replace them immediately upon taking office. There is little lost by using a recess appointment.
Is there something in the Constitution that says they can do that?