No, the police in the US cannot randomly search you in a train station. The only circumstance in which you can be searched without probable cause without consent in the US is by border security.
It seems that the US police would like to search you at as many locations as possible. In many cases this is not legally possible. However, the German police does not seem to have that attitude, or at least not that extreme. (Remember you are talking to an 18 year old who is not a lawyer.)
It is very apparent that I'm talking to someone who doesn't understand how the law works in the US. I don't hold that against you (why would I? I don't know how it works in Germany!), but I recommend that you develop fewer strong opinions about how things work here until you read a book or two about it.