1. Do we know the diameter or size of the Sun? What is our Sun's density?
The diameter of the Sun is 1,392,000 kilometers (its visible surface). This is 109 times the diameter of the Earth. It would take 1,300,000 Earths to fit in the Sun. The mean density of the Sun is 1.4 g/cm3, so not as dense as the Earth (5.5 g/cm3) and a little denser than water (1 g/cm3). The surface tempreature is 5,775 K. The density at the core is estimated to be 150 g/cm3 with a temperature of 15,000,000 K and a pressure of something like 340 billion times the pressure at the surface of the Earth (1 atmosphere). At this temperature and pressure, hydrogen fuses into helium, forming the power source of the Sun. A few more interesting facts: the surface gravity of the Sun is 28 times that of the Earth. The Sun’s rotation period is 25 days at the equator and 34 days at the poles (it is a gas, so can do that). While one would assume by models of the formation of the Solar System that the equator of the Sun should be in the plane of the orbits of the planets, it is in fact, tilted by about 7 degrees. Why? Not sure anyone really understands why!
2. If old stars are made of gas only, is the Sun old or young?
As noted in the previous question, all stars, including our Sun, are made of gas: everything in them is vaporized. The age of the Sun, ~4.6 billion years, is estimated from the radiometric ages of the meteorites (that formed when the Sun did). Its life span is inferred from a variety of theoretical and observational information to be about 10 billion years. Consequently, the Sun is “middle age:” about half way through its life cycle.