I wanna ask about a Russian word ‘брак’. As I can see it means ‘marriage’. But in German there is exactly the same word - ‘Brack’ which means ‘flaw’ or ‘smth rejected’. Is it just a coincidence or these two words have something in common?

Not really. In Russian the word “брак” has 2 meanings:
1) marriage
2) flaw
But they are not interchangeable, as you can see

Well, at weddings it is quite common to hear a phrase: “Хорошее дело браком не назовут!” (A good thing can’t be called ‘brak’) So it’s definitely a pun. But the two meanings of this word are not connected.

IT’S A COINCIDENCE!

The word “брак” meaning “marriage” comes from an Old Russian word “брашно” - delicious food, feast, viands. So it was the treatment usually served at weddings.

Today it looks somewhat like this: