Likely the biggest conflict is that between Maciek and himself in that he learns to live a lie, in particular that he is an Aryan and not a Jew, for so long and so well that in the end it basically becomes a reality. After all the horrific experiences he faced during the war, all the running and hiding and lying, even at war's end he cannot stop living the illusion in many ways.
This new Maciek, the Aryan one, eventually wins out and in many ways completely destroyes the old Maciek even as all the people who existed in his previous life disappear. Even as a child he appeared to have grown calloused and cold to strong emotion which served him well while in hiding but eventually blotted out any ability to feel much human emotion.
There are of course many other conflicts, for example the Germans constantly trying to expose Maciek and Tania and their efforts to conceal their true identities. There is also the conflict between Tania and Nowak who makes advances towards her and she has to fend him off and eventually flee.