How did the written Polish language survive in eastern Germany during partition (if it survived at all)?

By the time of partition, Poles had strong cultural tradition and literature. Suppressing such language and culture is difficult or impossible. You say children were educated in German". I am sure they were educated also in Polish, even if this happened at home. Certainly there were many well educated Poles by 1918, and overwhelming majority could speak read and write Polish.

Similar things happened in the Russian-annexed territory, which was the largest part of Poland. Russian policies varied with time, but there were times when formal education in that part of Poland was available only in Russian.

I can compare this with other nations whole langiuage was suppressed. Ukrainian language was never recognized in the Russian empire as a language, no official education was available, and at various time publishing books in it was prohibited, not even mentioning newspapers. Unlike Polish language and culture which are quite old, Ukrainian literature begins only AFTER Russian annexation, though most people spoke Ukrainian. So many books were published abroad and illegally brought to the empire. Even under such circumstances, by 1918 there were many people who not only spoke but read and wrote Ukrainian.

EDIT. I agree that the mass of peasants did not have a high literacy rate. The same applies to Russia and Ukraine where most peasants were illiterate; Poland was somewhere in between Russia/Ukraine and countries to the West of it. However for the survival of literary tradition, a critical mass of intellectual is crucial, and they can be a very small part of population. Intellectuals made a very small part of population in Russia as well, but they maintained a world-class literature. Polish literature had comparable status in 19th century if not higher, and nationalistic feelings were very strong both among the intellectuals and in the general population.

The "Germanization" process really only got underway after the unification of Germany in 1870. That means you have a period of only 40 years in which Germany is actively trying to suppress Polish culture. And in practice it wasn't very thorough.

I think you vastly underestimate the opportunity for and existence of "high-level" communication and culture in Polish in the Prussian-controlled territories. For example, the city of Poznán saw the founding (and persistence) of:

• the Raczynski Library ("the Library was still a mainstay of Polish culture under Prussian rule thanks to the Polish book collections and Polish personnel");

• the Central Economic Society for the Grand Duchy of Poznań ("Its main goal was to promote modern agricultural methods by organizing meetings, speeches, debates, excursions and competitions and also publishing the newspapers and magazines.");

• the Poznań Society of Friends of Learning ("When founded in the 19th century, the Poznań Society was the chief Polish scientific and cultural organization in Prussian Poland, and until the creation of Kraków's Academy of Learning in 1871–73 it was the most important learned society in all the Polish lands.");

• the People's Libraries Society ("Its main goal was to promote education in Polish language among the people, especially the lower classes, and to revert the Germanisation practices of the Prussian authorities. The society established a network of libraries, reading rooms and organized speeches.")

I get the impression that the imposition of strong Germanization after 1870 partly backfired, in that it inspired resistance among the Poles and a strong desire to retain and promote their own culture. This would have included things like home schooling in Polish, private schools for education in Polish, and the like. (The Russians outlawed private Polish schools after 1863, but Poles went ahead and set up illegal private schools in places like Warsaw anyway.)

(And I suspect even for those Polish-speaking kids who didn't have home schooling in written Polish, being literate in the Latin alphabet from learning to read and write German in school would get you about 90% of the way there -- sure, you don't initially know all the details of the orthography, but you know all but a couple of the letters and you know what all the words are supposed to be, because you already know the language.)

Finally, there's the fact that the relatively liberal Austrian-controlled Polish region (Galicia) was right next door; interested Poles could travel to Cracow or Lwow for a proper Polish-language university education, for example. (We have to remember that international travel in the 19th Century was generally a lot less restricted than it is now.)