Превод - Румънски-Английски - departamentul de procesare în cadrul firmei se...

Was it not better if it was translated "will be processed"? There is a conditional there "se vor procesa", if it is translated by "will process" it would have been "va/vor procesa". I see it like this.

And I set a hyphen in the Romanian text, maybe it makes more sense like so, azitrad.

Actually, I think more accurate would be:
"processing department - within the company, the following types of waste will be processed"

What do you think?

Yes, this is perfect.