Can my probation officer disclose my case to the public if I am a sex offender? Can they actually talk to non family members about my case?

If you are a sex offender your information is already a matter of public record.

Agree, I can look on internet and in most states and find the address of every sex offender.

They can investigate if they feel you are in violation, talk to people about your habits, who are you seen with. They would only do this, if they had reason to believe you were in violation of probation.