Well, unlike licensed psychiatrists, priests don't have to sign a doctor/patient confidentiality agreement to where you can sue them for releasing your info. Maybe the priest is considerate enough not to release information that you confided in him out of good faith, but you're basically leaving it all up to trust.
For mundane things, yes.
For crimes, a priest can reveal a murderer or serious criminal; and would certainly refuse to absolve anyone who did not turn themselves in.
In certain jurisdictions, they are required by law (like doctors, etc) to reveal crimes against children and other serious crimes.
Priests and the psychiatric community are bound by an oath of confidentiality. IF you are CONTEMPLATING a crime, they are bound by law to disclose this.