Let me ask you this. if the sun were so big and bright shining light through space when the earth would rotate and it would be night time for us why whenever we look in to the sky we do not see light in space from the sun shining? If it was the way they say it is then space around us would always be lit up and we would only be in the shadow of the earth when it would be facing away and we would still see light around the shadow.
Why would we still see the Sun's light? Are you describing something like how light leaving a flashlight becomes fully visible when there's dust or fog in the air? Space is a vacuum, light is only reflected from matter.
I don't think the sun would be so bright but yet it only shines on a little piece of the earth at a time and no where else.
A little piece of the Earth? Try HALF of it at a time.
And another thing, if the sun was so big and bright and so much closer than the stars in reality we should never be able to see stars at anytime because everywhere around us would be lit from the sun
Wrong. Light is not reflected from the
vacuum(itself) of space. Also, the Sun in your model is equally bright, no? (Or at least relatively speaking.) And much, much, closer. Indeed, why ARE stars visible in your model if this problem really exists?