a single hand grenade took out a German half-track, but in later scenes, the allegedly immobilized half track had disappeared.
It was the rockets of the Katyusha that were kept top secret, not the launching rails. The Russian propellant was more efficient than similar German rockets. This movie only has launching rails on the truck, no rockets.
There is a close-up of a pair of boots placed upon a hand grenade. The close-up shows the stitching pattern and design clearly. These are not WW2 German issued combat boots.