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

Do I need to send diplomas with my application?

Only if you are asked to. Some employers ask for a copy of your diploma at the beginning of the procedure; some recruit applicants without seeing it.

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

Employers normally ask for references or letters of recommendation.

All employers require proof of good conduct (i.e. whether you have a criminal record). Normally you need to be able to prove this for every job.