Is Dark Matter evenly spread out in the universe? Is Dark Matter evenly spread out? If no, could we ever find a correlation between the amount of dark matter and matter in a specific place?
 A: The existence of dark matter comes primarily from gravitational evidence - in other words, we predict some behavior because of the force of gravity, but we don't observe that behavior and infer that dark matter is to blame. Thus, most predictions for dark matter come from locations in the universe where there are massive objects which we can observe - for instance, Galaxies. Thus, the observational evidence is that dark matter is lumped in galaxies, galaxy clusters, and other conglomerations of matter.
The distribution of dark matter in galaxies is also not uniform - dark matter is generally denser in the center of galaxies then at the outer edges. So also in this sense dark matter is not evenly distributed.
If you mean on cosmic scales, then yes, there is not "more dark matter" in one large region of the universe then in any other. It is evenly distributed over the universe but in little globs where galaxies are. Think about sprinkling salt evenly across a table - the salt is evenly distributed but if you look closer there are regions where there is salt, and regions where there is none.
So in short, dark matter and luminous matter are generally found in the same location. 
A: Dark matter is not evenly distributed. It clumps together under its own graviational pull. In fact, it clumps first and normal matter clumps later. Look at the 3rd image on this site 
http://www.astronomynotes.com/galaxy/s10.htm
To see an example for dark matter distribution.
A: Dark matter doesn't have "gravity" but is simply a theory to explain Gravitational abnormalities in the universe.  Gravity itself is a theory with several holes that need to be addressed most importantly why the universe is still expanding "speeding up even " when gravity should have it collapsing back on itself billions of years ago. The interaction of weak and strong forces isn't completely understood either. Here is a good write up with a new theory of gravity that doesn't call for a dark (undiscovered and unproven ) particle to close holes in its theory. It is just a theory as well so "FLAME OFF" .
