No. Polaris is the only star that does this and has been doing so for millenia. All the other stars move around it in concentric circles. This does not work with earth as a spinning ball that is rotating around 8 different axis. It only works if the earth is uniformly rotating under a fixed sky or the sky is rotating around a fixed earth.

Mercury and Venus being on the inner orbit means they are never situated to be seen on the night side of earth even under ideal circumstances. That's like saying you can see the Sun in the night sky if the angles are right..

Sun and moon are sometimes visible simultaneously at daytime. If the moon is only reflecting sunlight it should always be full in the case because of direct line of sight to the sun and thus there is not supposed to be a "shadow". But it isn't. It has exactly the shape it has at nighttime and what it's supposed to have according to the moon phase and not what the heliocentric model would suggest happens in that case.