If Earth is tilted, why is Polaris always above the same spot? Why is Polaris, the North Star, always above (or near) the North Pole? If Earth is tilted, Polaris' path should be in winter 23 degrees away from its path in summer, or not?
You are correct that the axis of the Earth's rotation is tilted with respect to the plane of its orbit by 23 degrees. But it is incorrect that the direction that the axis points changes by a large amount (it should be 2*23 degrees) over a 6 month time span.



Your assumption: If axis it pointed at Polaris at (1), then it should be pointed at a different star at (2).

The axis remains pointed in the same direction throughout the entire year because the laws of physics are that the axis of a spinning object remains pointed in the same direction unless a torque acts on the body to change its orientation. There are torques acting on the Earth (namely the Sun and Moon), but it takes 13000 years to change the direction from "one way to the opposite way", not 6 months.



Correct: The orientation of the Earth's spin axis remains pointed at the same star throughout the year (ignoring the slow, 26000 year precession cycle).