And another picture where each successive light is smaller and smaller:

Test it for yourself with a ruler.

I have to see some evidence of this "Sun looking twice as big near the horizon" claim. If anything, the Sun is either the same exact size near the horizon as it was in the middle of the sky, or slightly smaller or slightly squished vertically, based on what I've seen. I don't know if a spotlight sun is widely accepted by the FE community. I certainly don't think it is a spotlight, and from what I see, there is a gradual transition from day to night. The further the light travels, its color changes due to interaction with the atmosphere. Shortly after the red wavelength, it becomes invisible. The atmosphere isn't perfectly clear, it's opacity, and the distance to the light source, is what causes the darkness of night.

As for why it appears to go under the horizon seems to be chalked up to not knowing what a 300mi diameter object looks like as it goes overhead. If you watch a plane fly out over an ocean, even though it may be maintaining its altitude, it appears to be heading down to interact with the horizon before it becomes invisible due to the atmosphere. The assertion is we simply don't know how an object like the Sun would appear if it is beyond the vanishing point.

The plane also gets smaller as it flys away.  The sun stays constant for the time of year.   Why does the sun not get smaller?  Mountains get smaller as you drive away from them and they are pretty big.  The sun should be half the relative size as distance doubles.