No, not many in Germany but Berlin has some "Hotspots". It's a few thousand people. But in university, we have/had many exchange students over the years.
Yes, it is government-funded. Or let's say funded by the people with income (you pay around 50% tax). You get the apartment (which has to have an appropriate size) which should be around 500-600€ in cities like Berlin, which means another 230k-270k directly to the landlord and then you have 230k for food, electricity, whatever. Electricity is around 9k, Internet 9k, going out in a bar costs not much more as you guys paid for your meal. So the normal student life is not that expensive. 230k is also the minimum income for a student job (by law).
This is why many people don't want to work in low-income jobs (it is better not to work). Government money is not a good incentive. The thing is that you are not allowed to work or study when you get government checks. You sit all day long in front of the TV and eat fast food. So it's not universal basic income. You are not allowed to make money. As a student you need, a job. Universities are free, except a fee for stuff like trains, busses and so on. The expensive stuff is healthcare. You pay 55k for health insurance a month. And well when you want a "normal" life with a car and stuff it gets expensive.
What are you doing for your master?