What are basic observations about the universe that any theory of cosmology must explain?

Answer 1

read these:
http://map.gsfc.nasa.gov/m_uni.html
http://www.astro.ucla.edu/~wright/cosmo_01.htm

Answer 2

Where does mass come from? What is mass composed of? What is the effect of a sun upon a planetary system, and how did that system form? What are the basic forces acting upon matter now and how would they affect past conditions?

That is a general idea. None of it will make any sense to a person if they do not begin with Creation. The very first question is the hinge to all the rest, and it cannot be answered apart from Intelligence greater than our own.

Answer 3

1. The general expansion of the Universe, and the rate of expansion.
2. The relative abundance of Hydrogen as compared to Helium.
3. The current 2.73 K microwave background, and implications for the age of the Universe and presence of dark energy.
4. The rotational rate of galaxies, and the implied presence of dark matter.

Answer 4

The origin of the laws of physics.
The origin of the mass of the universe.
An explanation as to the origin of the "space" in which these items exist.
An explanation of the relationship of these items and how they achieved their values.
And how did these things spontaneously appear.

Answer 5

I can think of two:
1) background radiation
2) red shift