In theory, is there anywhere in the universe where velocity=0? Earth is traveling at a certain velocity.  Earth orbits the Sun at velocity X.  The sun is orbiting the center of our galaxy at velocity Y.  The galaxy is orbiting (something?) at velocity Z. On and on... 

In relation to zero, Earth has a velocity of X + Y + Z + (?).

Is it theoretically possible that there would be a point in space where nothing is moving and velocity is essentially 0?  

If so, what would time look like at this point in space?
Yes.

The velocities you list (X, Y, …) are all velocities with respect to some reference frame. But all reference frames are arbitrary, and you can always define a reference frame where the velocity of some object is exactly zero, as long as it's not accelerating.

For instance, Earth's velocity in the Sun's reference frame is X, but in its own reference frame, it's zero.

This is not just semantics; it is probably one of the most profound concepts in physics that there is no such thing as an "absolute frame of reference". Before Einstein, people thought that time and space are absolute, but Einstein taught us that everything is relative.

In cosmology, there is a special reference frame in which all matter on average is zero. The coordinates of this frame are called comoving coordinates, and in many cases it makes sense to regard this as the most natural reference frame. But it is important to remember that it is still just a choice, and that any other reference frame is equally legit, although a bad choice of reference may make certain calculations harder or impossible to solve. In comoving coordinates, the cosmic microwave background (CMB) is isotropic, i.e. it looks the same no matter which direction you look. But since Earth is traveling with a non-zero velocity in comoving coordinates (at an average of 369 km s$^{-1}$), the CMB is slightly blueshifted in the direction in which we're traveling, and slightly redshifted in the other direction.

What would time look like? Time runs slower, the faster you move. In any non-accelerating reference frame (an inertial system), time runs "as it should", but an observer in this frame who measures how time runs in a frame that has a non-zero velocity with respect to his/her frame, will see it run slower.