The German tank which appears near the end of the film is a replica of a Panzer III which was created by modifying a Swiss Panzer 61 tank. It was one of two such vehicles previously used in Enemy at the Gates.
The object the Bielskis take from their house is a mezuzah, a piece of parchment (often contained in a decorative case). A mezuzah is affixed to the door-frame of Jewish homes to fulfill the mitzvah (Biblical commandment) to inscribe the words of the Shema "on the door-posts of your house". The parchment is inscribed with specified Hebrew verses from the Torah (Deuteronomy 6:4-9 and 11:13-21). These verses comprise the Jewish prayer "Shema Yisrael", beginning with the phrase: "Listen, Israel, the Lord is our God, the Lord is One."
At the very beginning of the movie (around 40 seconds in), after the "Germany occupies Belarussia" information, there is a shot of a column vehicles entering the bridge. This is an excerpt from the Nazi war film chronicles ("UfA-Tonwoche") from September 1939. It shows Adolf Hitler's visit to the conquered Polish city of Gdynia, Poland's pre-WWII biggest military and merchant harbor. Specifically, it is the moment when Hitler's convertible car crosses overpass on the way to the harbor part of the city.