First, light is a property of electrons in atoms. Light is fundamentally limited to the size of atoms at their smallest resolution. Visible light, x-rays, or any other radiation is simply unable to peek at the components of atoms because of its nature. Radiation (light) is the result of the change of electrons from one energy level in an atom to another. Anything smaller than an atom, such as elementary particles, cannot be seen so its size has to be inferred.
Elementary particles each exist at a discrete point in space. They have no width. They are separated from each other by forces that exist between them, but they are not solid little billiard balls. When a diameter of a particle is given, it is really the distance they separate from each other, not the same thing as the kind of diameter macroscopic objects would have.
There is a certain limit, the Planck length, which is thought to be the smallest possible length in the universe. It is 1.61619926 × 10-35 meters and is derived from calculations. You can think of it as the absolute minimum grain size of the universe. Even if it were possible to have such fine resolution, it would be the ultimate pixel size.
Yes, there is an ultimate limit to how small a thing can be.
As for the universe being completely fractal, it's close. In a certain sense there are similarities between the very small and large, but you will not find a galaxy in an atom. The similarities are because the small, the large, and in-between are all governed by similar forces that follow similar laws. Where there are differences, that is because different laws apply.