Definitely not really true. Under 15% of students receive BAFÖG [1]. No idea where you got the idea that German students get free housing at many Universities as that couldn't be further from the truth considering that there are only enough rooms for around 10% of all students [2] and those are definietly not free, although pretty cheap. However many struggle to find an Apartment, especially in bigger Cities like Berlin or Munich.
I said many, not all :). You're right, housing isn't free, but if you get student housing it's usually less than the monthly stipend thus free for the student.
not really. The average monthly stipend (that only 15% even get) is 579€, which is arguable not enough for rent in most bigger Cities (and that is ignoring that you also need to eat).
The vast majority of students are either financed by their parents (the stipend is dependent on their income and if they earn more than a certain amount they a legally obligated to help their child) or by themselves. In Germany the university is mostly free (a couple hundred euros a semester), but most definitely don't live for "free".