Do PhD students (who work as research/teaching assistant and get paid according to the TV-L E13 bracket) in Germany get an official student enrollment from the university 'Immatrikulation'?
Depends. At my university in Germany, you could choose yourself if you want to enroll or not. Some enrolled, e.g. for the cheap bus ticket and student lunches, other didn't. But there is no general rule for that, every university or even every institute might have its own regulations.