Legal Question in Criminal Law in Utah

if a felony you get a jury trial unless specifically waived. If a misdemeanor, you must request one. As an attorney I always request a jury when I make my appearance.

Public defenders are appointed or not usually at the first appearance where there is a judge. If a misdemeanor, at the arraignment. If a felony at the "first appearance". Different courts may call them different things. Sometimes they will be appointed later if the defendant initially wants to hire counsel and later finds out he cannot, or changes his mind, etc.