As a German I can assure you that false friends are something you scare away all pupils (regardless of age). I have very intense memories of our English teacher correcting us again and again.

Regarding the composita in German: we are moving more towards the English approach by splitting these word monstrousities with hyphens. E.g. Donaudampfschifffahrtsamt may be spelled Donau-Dampfschifffahrts-Amt. Its way easier to read and write. While the hyphenated spelling is not something that is used often officially, it got more popular in the last decades.