Why a gravitational lense makes multiple distinct pictures of a distant object rather than making a symmetric ring? I cannot imagine how a group of galaxies may produce pictures of a distant object on a ring-like region that is not symmetric. Why there are empty parts of that ring where there are no pictures of the object? Could there be a so intense disbalance in gravity inside that space to cause a deformed or 'broken' ring?
 A: For simplicity let's suppose the lensing is strong and the lensing object is a point mass. When the object is perfectly on the line of sight between the Earth and the source, you get an Einstein ring:

However, in general the object is off the line of sight. In this case you get two separate images: one from the light that basically goes directly from the source to Earth, and another from the light that goes near the lens and gets deflected to Earth. That is, you get one image roughly in the direction of the source, and one image roughly in the direction of the lens.

You can get more complicated stuff when the lensing object isn't a point mass, such as a partial circle or four images, as in Einstein's cross, but I hope this gives the basic intuition.
A: This is not an answer, I write this in the hope that someone who does know is triggered to write what is actually going on.
My speculation is that what is with a general term being referred to as instance of 'gravitational lensing' is in many cases more fittingly described as 'gravitational mirage'.
Mirage is apparent displacement of a scene as a whole; it does not involve magnification.
In the case of a mirage the light travels through a region of air where there is a density gradient perpendicular to the direction of propagation. In air the speed of light is slightly dependent on the density of the air that it is traveling through. The resulting bending is minute, but if the distances traveled before and after entering the light bending region are large the apparent shift of the location of the scene is significant.
Hence my speculation: gravitational mirage.
