The effect of the T-Rex works just as well if you are stationary and the T-Rex is rotated in position. So it would work at any distance as long as you could still distinguish the features of the T-Rex, say through a telescope.
That is not recreating the scene.
And in the case of the sun, it is the earth that is rotating in order to change apparent position in the sky of the relatively stationary sun, so no, the sun would not need to change its distance from the earth to create the perspective effects referred to in this thread.
No. The sun would need to change its distance to you very significantly if we are going to say that it can change its angles like the end of a long hallway. A rotating earth doesn't change your distance to the sun. It's really just a rotating camera. Rotating your camera around doesn't change perspective angles of distant bodies.
The angles don't change between the two railroad tracks in a railroad perspective scene when the camera makes a 360 degree roll upside down, nor does the angle between the vanishing point of the railroad track and a streetlight above your head change when the camera rolls around. The angles between bodies do not change at all.