Does Polaris have a trail in the sky timelapse? Yes. Every star has a trail, but it's smaller if it's closer to the pole. Polaris is close to the pole but it's still 45 (arc)minutes away. I don't think it's visible with the naked eye; no star trail is visible with the naked eye as you only see one 'instance' of the sky. What perhaps would work, and is more feasible for stars closer to the celestial equator, is trying to see the movement of a star compared to an object on Earth, e.g. a tree, a building or the horizon.
The exposure times of the photos are different, as @J.Chomel notes in the comments. You can calculate the exposure time by looking at the arc length; in 23 hours and 56 minutes (a 'sidereal day'), a star will make a full circle.
The trails on the last photo have an arc length of about 8 degrees, corresponding to about 30 minutes; the first two photos are more like 9 resp. 5 hours. Also, the zoom factor (of the lens) may play a role; if a photo is zoomed in more, Polaris' movement is more likely to be visible. I'm not sure if this plays a role in this photos, though.