The moon’s orbit around Earth is not a perfect circle so it can be as much as 7% bigger or smaller than average depending on the cycle. On a clear, calm night, the moon always “seems” bigger when it is low in the sky due to perspective and how your eye compares the size to objects near the ground!
To confirm this, simply take a picture of the moon when it is low in the sky and seems large. Don’t zoom in. Then take a picture of it when it is high in the sky. You’ll see that it is the exact same size.
Particles in the atmosphere like dust, pollution, pollen, smoke and even water droplets do tint the sun and moon. Typically when the sun and moon are high, they appear white. The light passes through a thin layer of atmosphere. When they are low in the sky they pass through much more air and that filters the colors to allow the dominant colors of red, orange, and yellow to be more prominent.
If you’ve taken a picture of the full moon and noticed a bright object in the picture that you didn’t see in the sky, here’s what it probably was.