Italy - diplomas, references, recommendation or proof of good conduct

Do I need to send diplomas with my application?

No, but bring everything with you to the interview (Italian bureaucracy is very strict).

Should I supply references, letters of recommendation or proof of good conduct?

It is always an advantage to the candidate to provide references or letters of recommendation (from previous employers, university professors, etc.) to support their previous work experience or testify to their skills and abilities.