Should blue and white stars appear red and inflated while observed on the lower part of the night sky for the fairly same reason as the sunlight during sunset? As these stars emit blue light frequencies along with other frequencies the blue component should be scattered the most even for stars shown on the higher parts of the sky... then the yellow and green so for the lower sky stars the only color that should reach us as in the case of the sunset light is the red color. But fot the stars the image of the star in our eyes should form a pattern similar as the sunset light on the very proximity of Earth surface where we spot a very long red bar along the horizon with the Sun in its center.If all the pressumtions in my question are wrong I kindly ask why in a possible answer to my question....
You're correct that the light from stars can be scattered in exactly the same way, such that some blue part is removed, leaving relatively more red. But the exact optical effects that you describe are not common.
The flattening of the sun near the horizon is only possible because the sun is an extended object. Light from limbs which normally are further apart in the sky can get compressed due to the atmosphere. Stars are not extended objects. While the light can be shifted around, it isn't normally blurred to our vision.
At lower light intensities, our eyes are less sensitive to color. So the color shift from atmospheric scattering happens with starlight at times, but it harder to notice than it is with bright sunlight.
Without practice, few stars have sufficient color shift to be noticed as anything but "white". Shifting the color just a little bit redder is normally less than can be perceived.
The sun is very easy to see within a degree of the horizon, where scattering is greatest. It's often quite difficult to see stars that close unless you're in a very dark area. Even 5 degrees of elevation will greatly reduce the amount of scattering.