"Streetcars run to all four train stations."
Translation:Ke všem čtyřem nádražím jezdí tramvaje.
The "do" would mean that they stop in the station. Here, it is literally meant that they stop nearby, since streetcars don't go into train stations. You indeed usually say "Tramvaje jezdí do všech čtyř stanic." but what you mean is that they "jezdí do všech čtyř tramvajových stanic".
True, except that "tramvajová stanice" (a tram station) is rare - a place with multiple platforms, a roof, or any kind of greater infrastructure than a regular tram stop ("zastávka") has. Prague doesn't have tram stations, only tram stops. I can't be sure about other Czech towns - perhaps the mixed bus/tram station in the center of Liberec qualifies (it's actually labeled as "Terminál MHD" on the map).