I am an open-minded Indian student and I will be going to Germany to join the University of Bonn for my masters in Computer Science. I have planned a monthly budget of € 830 including studentenwerk fees, which the university noted me will be no more than € 350. Old students say that it averages to € 250 or something leaving me with € 580. Will that be sufficient for me to eat for a month at a Mensa (I plan to cook in the evenings though) or say maybe watch one movie a month or maybe take a weekend trip to Köln?
I've been living in Bonn for about two years now and have a monthly budget that is lower than yours (750€), but I find that this is more than enough for a relatively normal life. You should be fine as long as you live in a Studentenwerk dorm; I myself live in such a dorm and have to pay about 300€ monthly (a fee that includes both rent and utilities).
You also have to pay semester fees to your university, but that's just once a semester and it's not such a big deal (~250€ in general).
By the way, I am a scholarship holder, so I didn't mention health insurance as part of my costs; the DAAD is paying this for me. You should count on about 80€ for that as well.
Less than a decade ago, I lived in Bonn as a student for less than 500 € per month, doing pretty much what you describe. I do not know the exact numbers as I had more money available (I simply did not spend it). As inflation was not that bad, what you try to do should be possible.
However, here are some points to consider:
In the last years the German equivalent of high school has been reduced by one year in many states of Germany which lead to twice as many people finishing high-school in recent years. As a considerable number of these people study afterwards, this has lead to a temporal increase of the number of students and thus to a housing shortage specifically for students. After what I heard, Bonn is affected particularly strongly by this. This may increase the rent you have to expect.
The easiest way to obtain a cheap accomodation is from the Studentenwerk. It may help to apply as early as possible and look for out-of-schedule offers from them regularly. In particular, they may have a contingent of appartment that they only rent to foreign students and are thus not affected by the previous point. Another advantage is that you do not have to hassle with organising electricity, heating, Internet access yourself as you often have to with privately rent appartments.
I do not know how health insurance works for foreign students in Germany. As I am German, it was free for me. This may cause some additional costs for you.
The above assumes that you only consume what is necessary for life (and maybe not the cheapest food). E.g., if you consume relevant quantities of alcohol, coffee, cigarettes or other drugs, you have to take this into account.
Assuming that this is what you are referring to with Studentenwerk fees, there are fees of about 250 € that you have to pay once per semester. While you must pay them, they grant you free access to public transport in all of North Rhine-Westphalia (with the exception of high-speed trains) and reduced prices at the student canteen (mensa) amongst others. So, travelling to Köln is free. Something similar holds for most if not all German universities.
I am an international master's student in Berlin. According to this, Bonn is a tiny bit cheaper than Berlin on average. I live pretty comfortably on €900 per month all inclusive, and I am pretty sure I could get by with less. The big question is rent, which costs me something like €260 pm. So I would say you'll be fine.
I'll add that I have to pay compulsory membership fees for the student union every term. I have to pay mine in a lump at the beginning of the term, something like €360 for the semester. Check with your university as this was a little bit of an unpleasant surprise.
I originally answered the second, slightly off-topic part of the question. I agree it is not on-topic for academia.se. I have edited it out.