How would you prove to them that earth orbits the sun? The sun will last, at its current brightness for 9 billion more years. The sun's spectrum is very complex, and indeed there are a lot of lines—both light and dark (emission and absorption)—amidst a sea of what looks to be continuous frequencies.
It's consensus that the very similar apparent sizes of the moon and the sun as seen from earth is a coincidence (as already answered in this site). You say that sun rises in the east (with a certain degree of oscillations due to the tilt of the axis) just because the earth. Assume you're talking to someone ignorant of the basic facts of astronomy.
How long until the sun gets burned down to the point where it cannot sustain life on earth anymore? What are the main factors which determine the. On the other hand, if the water were completely still, with a smooth and horizontal surface, then the sun glitter ribbon would be gone, and you would just see a direct mirror. The sun would actually look very small to us in the sky if there were no atmosphere (it's the same.
Similarly, how would you prove to them. Those are completely different things. The core temperature of the sun is on the order of 15 million degrees kelvin while its surface temperature is around 6000k. As i asked before, separate.