Part-Time PhD in Germany
Most PhD students in Germany receive a regular salary, not a scholarship, and are officially employed as research/teaching assistent (this is what full-time/part-time refers to). It depends on various things like the source of funding if these positions are full-time or part-time.

The time you dedicate to writing your PhD thesis is technically your own free time. So there is usually no difference between these positions in terms of workload, value of the degree, etc, except for the salary. It's stupid, I know...

There are calculators on the internet that can tell you the exact salary, but lots of public charges depend on your personal situation (whether you have children etc) and things like where in Germany this is: http://oeffentlicher-dienst.info/c/t/rechner/tv-l/west?id=tv-l-2016i

For a 65% position it's currently ~2200 EUR/month (after taxes a bit less than 1500 EUR).