Some calculations.

[Equiliari]

A ship 10km long would certainly have its own center of gravity.

Well yes, anything with mass will... But it would be so minuscule that it would be of no significance. Remember, we are talking about the weakest of the four fundamental forces in nature. Gravity is calculated by the formula (G*m1*m2) / r^2, where "G" is the gravitational constant. "m" is mass of the object in question. The "r" is the key point, being distance between the objects. As pointed out, the distances between objects in an asteroid field are massive. Gravitational attraction would not be a problem for a 10km long ship in an asteroid field.

The hull needs to be appropriated to all the shit that will be orbiting around or sticking to it on its journey.

In all seriousness, a ship 10km big would not work very well forthe kind of warfare depicted in StarCraft. And the size itself is insanely big. That part we agree on fully. The only thing I had gripes with was that an asteroid field would pause a threat to a 10 km big ship, which it would not. The asteroids and particles are just too far apart to pose a significant danger.
Traveling in space nearing the speed of light would be far more of a deterrent for this ship than an asteroid field. And that counts for any ship size.

That might include smaller asteroids that feel the need to bang into it at high velocity - sort of like a meteorite entering earth's atmopshere, except that a behemoth has no atmosphere apart from a shield - and if the shield is anything like the defense matrix, it doesn't last long and needs a lot of power; the sort of power that slowly recovers over time.

The hull would have to be strong enough to protect from any particles the ships sensor system could not detect. Otherwise, there should be no major problem with foreign objects. All depends on the object. A ship that size would have included countermeasures (and significantly improved sensory system than we have today), be it the defense matrix, cannons or avoidance maneuvers. Most likely, a direction would be pinpointed before its entry into the field neglecting the need to maneuver. Only needing to periodically turn on the defense matrix for some milliseconds to deflect tiny particles... well, depends on how the defense matrix works. And blast asteroids that get too close with the ships cannons.

And isn't uranium an element? Why would they call depleted uranium an alloy (an alloy is just a compound with metal properties and solid in earth atmosphere and environment, far as I know)?

Uranium is an element, yes. A metallic element that can be used as an alloy:
http://en.wikipedia.org/wiki/Staballoy