No, a star cannot be in the exact same place in the sky two nights in a row from a human observer's perspective. The apparent position of stars in the night sky changes continuously due to the rotation of the Earth on its axis. This rotation causes the stars to appear to move across the sky in an arc over the course of a night.
As the Earth rotates, different stars become visible at different times, and they appear to rise in the east and set in the west. The apparent movement of stars across the sky is due to the Earth's rotation, not the movement of the stars themselves.
However, over longer timescales, the positions of stars do change due to their own motions through space. This is known as proper motion. However, the changes in position due to proper motion are typically very small and cannot be noticed over short periods, such as two consecutive nights.
It's worth noting that some celestial objects, like the planets in our solar system, may appear in roughly the same area of the sky for several nights in a row due to their slower apparent motion relative to the stars. But even in those cases, their positions will still change gradually over time.