tl;dr. I think it's unrealistic at this stage.
Note that the Masters degree in America is different than in Germany, in the sense that bachelors are typically longer and the Master and PhD are somewhat parallel in something called 'graduate school'. One question that arises is to what purpose do you want a Masters? Are you interested in doing research on the longer haul? Then it's a PhD you need. Are you mainly interested in the prestige?
My advice, if you are interested in doing academic research would be to already find a German university that will accept you in a Masters program (I don't know if it's possible...). You will be better armed to apply for a prestigious American graduate program.
More precisely about your concerns:
It's fine, people start grad school later than that.
Nationality is a non-issue providing you are accepted in a program and have secured funding (see below). If anything it might take a bit longer for visa procedures, certainly not a killer criterion at any rate.
university in Germany,
German institutions are generally highly regarded in America, the problem is not Germany, it's the type of your institution. A German 'university of applied science' (Fachhochschule) delivers vocational degrees. The focus is to give graduates a set of practical skills so that they can enter the workforce directly upon completion of the degree. It does not prepare you to enter a prestigious graduate school, whether in America or anywhere else. When applying, you will be competing with people who are far better prepared than you.
Top American graduate schools give a enormous importance to recommendation letters. It's already hard to find professors at German/Swiss universities who know enough about the American recommendation culture to write something competitive, I suspect few (none?) of the teachers at a Fachhochschule have experience in that matter.
You will need funding. For Masters you already realized how much tuition you will have to pay. Many student fund their studies with loans, and in the business schools it's common for employers to pay tuition. Departments sometimes pay tuition.
For PhDs, It's (almost) never the case that graduate students pay tuition out of pocket, that's also a reason why these programs are so competitive. Your potential adviser will have to secure hundreds of thousands of dollars to pay your tuition and stipend. For the reasons listed above, I think you will struggle to find funding, but it's unrelated to your current account balance.