Do judicial appointments have to be signed by the president?
Yes, the President must sign judicial appointments because they are the final step after the Senate has provided its "advice and consent". The President nominates a candidate, the Senate confirms the nomination, and then the President formally appoints them to the bench.
Nomination: The President selects and submits a nomination for a federal judgeship to the Senate.
Confirmation: The Senate then reviews the nominee, and a majority vote is required to confirm the appointment.
Appointment: Once confirmed, the President officially appoints the individual to the position by signing the appointment document. The U.S. Constitution gives the President the power to "nominate, and by and with the Advice and Consent of the Senate, shall appoint… Judges of the Supreme Court, and all other Officers of the United States".