I was under the impression that "Kindergarten" was moved into the English language, much like "Hamburger", "Schadenfreude" and "Rucksack".
It has, but only in American English (presumably due to German immigrants to the US). In the UK we call kids' first school "Primary School". It's definitely possible that a European from another country would translate "kids-first-school" into Kindergarten if they learnt American English, but a brit if I read "kindergarten" I think "either German or US school" and I would expect people from other countries to leave the term untranslated if they were referring to their local schools.
Primary school is 5 - 11, no? That would be Elementary or Grundschule. Kindergarten is for 4 or 5 year olds, like pre-school.
I think you're right. But that only proves that I didn't know what the word meant!