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This sentence could be translated:
However, "on" is not necessary (we usually skip personal pronouns if it's obvious whom we talk about).
"Zadanie" is a concrete task to do only once, while "praca" is a bit longer, constant job or work, or even a piece of art is called "praca".
(3) "na tę pracę" wird verwendet, wenn es um Arbeit im Sinne von Erwerbsarbeit geht; bzw. um das Werk eines Künstlers.