First, CNR is a giant entity with a hundred units, spread across all Italy, and with about eight-nine thousand researchers. It is therefore quite different from a university.
- Yes, there are public competitions. All available calls can be found here.
- In principle, technologist and researcher are two different paths. A technologist is a kind of senior technician. However, the distinction between the two paths is frequently fuzzy. For researchers, the career progression is Researcher (equivalent to an Assistant Professor in the university system), _Senior Researcher (equivalent to an Associate Professor)", and Research Director (equivalent to a Full Professor). For technologists, the career progression is Technologist and Senior Technologist (as far as I know there are no further steps). You move from one level to another through competitions.
- CNR staff does not have any teaching load, it's a research only institution. Some researchers, though, are also affiliated to universities (and some CNR units are hosted by universities) and may teach classes. The salary between CNR and universities is about the same.