I could imagine that the people and kids in that city have had a good amount of exposure to the German language.
No, not necessarily. Of course, Germany influences Szczecin, but I'd actually say that German is more used in Gdańsk than in Szczecin due to the huge amounts of German tourists visiting. Stettin never really had the same place in the German heart as Danzig did. English is probably spoken more than German in Szczecin, anyway.
Would you expect Russian and American kids to be bullied in Polish schools as well?
American, probably not, as everyone has a fairly favourable view of the USA. Russian kids - yeah, there are issues with kids from the east and Polish schools.