If the moon rises right after the sun sets, it is likely to be lit by sunlight as a full moon. An AU is about 150 million kilometers. We don't travel at a constant speed on our orbit around the sun. The Earth's orbit is elliptical, not a perfect circle. Kepler's second law says that we move faster in our orbit the closer we are to the sun.
Astronomy is the organized study of the universe above the Earth's atmosphere.
The celestial sphere is in the mind of the beholder. It is an imaginary surface on which the stars and other heavenly bodies are plotted. Because of the Earth's rotation, stars rise in the east, just like the Sun does. Tycho Brahe carefully recorded the positions of Mars and other planets without the benefit of a telescope. No, but he perfected it and used it for the first time to record the appearance of the Sun, planets, and some of the planets' moons.