[...] I am wondering: if I am not a citizen, let's say of Germany, can I avail of the same tax rate if I will stay in that country or do I have to be a legal resident first? I understand that with USA even if one is living in another country as long as they remained to be US citizen then they are subject to the same USA tax laws.
You can be a legal resident of Germany without being a German citizen. If as a result you have to pay your taxes in Germany, you'll also get the tax benefits that come with it. However if due to some tax treaty between Germany and your nation of origin you still have tax obligations to your home country -- as, to some extend, seems to be the case with US citizens -- you're shit out of luck.
I happened to live in a country where the government has not yet focused on implementing tax codes on cryptocurrency but I am suspecting that exchanges are the ones collecting the tax when we convert our Bitcoin into the fiat money, which can be convenient for all of us. [...]
I wouldn't get my hopes up for exchanges taking care of collecting taxes for you. If it were only about capital gain taxes, maybe. However in many cases income tax applies, which exchanges are not able to determine due to not having insight into your income and tax status. Add to that cryptocurrency being a global phenomenon with people from various countries trading on exchanges of varying legal status it is close to impossible to find a one-size-fits-all tax collecting solution, unless the exchanges operates and focuses on only a single tax territory.