Final answer:
Based on the characteristics described, the astronomer is observing a galaxy, which rotates, spans millions of light-years, contains both young and old stars, has an irregular shape, and contains dust and gas.
Step-by-step explanation:
The astronomer is likely looking at a galaxy. Galaxies are massive systems consisting of stars, stellar remnants, interstellar medium of gas and dust, and dark matter, all bound together by gravity. Key indicators that the observed object is a galaxy include its rotation, vast size spanning millions of light-years, the presence of both young and old stars, its irregular shape, and the fact that it contains dust and gas. While black holes like the one at the center of our Milky Way galaxy, planets, and comets are all fascinating celestial objects, they do not match the description of being millions of light-years across and containing a mix of stellar components. The correct answer to the given characteristics is c) A galaxy.