Why are many (revolving) structures in space mostly flat? Like galaxies, planetary orbits, or Saturn's rings.

Two objects that orbit in different planes can encounter each other at high speed, so those orbits are not stable - only orbits in the same plane are stable. Even within one plane, different noncircular but intersecting orbits have opportunities for encounter and perturbation - these also leave matter in more circular orbits or eject it completely. The result is concentric nonintersecting orbits, where each particle has velocity differing only slightly from particles in neighboring orbits.

Based on your answers can I say it this way, That if the whole glob is rotating along the Z axis(vertical) the stuff at the poles is not accelerating (as in orbit around the center) and gets pulled into the center & only the stuff in the rotating disk 'survives'? I may be wrong.

Disclaimer: I don't have a clue what I'm talking about, from an astrophysics perspective.  I'm just trying to connect some basic topology to the question. Because a solid 2-torus (you can think of "thickening" an annulus) admits an everywhere continuous map from itself to its tangent space, a 3-annulus (don't know the real name of this, maybe that works, just think of the thick "skin" of a ball, or, say, the earth without its innermost core) does not.  This means that if everything in your "clump of stuff" is revolving together in a continuous way (following the continuous vector field on your space), it can do it if the space is a 2-torus, but not if the space is a 3-annulus, because you'd have weird stuff happening at the poles (assuming a regular rotation about a centered axis). The fact that a thick disk (topologically, a 3-ball), which is the 2-torus with the "donut hole" added back in, does not admit such a mapping can be thought of as why things get weird at the center of galaxies that rotate (black holes).  The same thing happens for the 3-annulus (if we ignore the center of objects like pulsars for a moment) --- things get weird at the poles (**** blows the **** out of them real frigging hot).

It's least complex, from the point of view of the center.  As the density gets higher, it's most efficient to confine the orbiting matter along a plane going along in the same direction.

Rotation alone is not going to make an object spherical. In three dimensions, any rotating object will become oblate spheroid, and will asymmptotically become flat, 2 dimensional ball (disk). In three dimensions, a rotating two dimensional object will asymmptotically approach an one dimensional ball (a line), if the axis is a line and is not normal to the body itself (i.e. has one basis vector such that the scalar multiplication of the axis and the basis is not zero). The reason is, there is a centripetal force, which wants to maximize the equatorial (equator computed w.r.t. the axis of rotation, being the largest intersection perimeter of the object and the plane normal to rotation axis) radius of the object . But the object has finite volume, thus maximizing this will make the extension along the rotation axis minimal. That forces an N dimensional rotating object in three dimensions with the condition that there exist at least one basis vector with a none zero scalar product to the axis to approach N-1 dimensions. In 4 dimensions, rotation happens along a plane. So the 4 dimensional object will havve two such basis vectors, and will ALSO approach a disk. A three dimensional object in 4 dimensions, with two such spanning vectors will approah a line. Rotation is a two dimensional pheomena. All higher dimenstional objects thus approach a new shape which can be embedded in two dimensions, thus lines or disks. Sphericity has to do with self gravitating, and minimizing the self potential. If an external object is gravitating, then the total potential w.r.t that object is large, indeed, for a disk, but the rotational process will come to stabilization at the maximal radius as described above. That is the case of a ring (Saturn is gravitating as the dominant) or a galaxy (no primary dominant gravitator.)

I would--since the word magnet was not found on this answer page but the angular momentum seems well postulated--like to point out that if you look at a hydrogen p orbital find that the magnetic moment is responsible for the bubbles on the top and bottom and that it looks a lot like the Milky Way with the majority of mass in a disk shape but some of the distribution (see Fermi bubbles) in a dual symmetrical bubble shape. I would imagine this is the reason you see things in a disk shape and I beleive that the magnetic moments of each solar system--especially where you have very strong magnetic fields associated with magnetars--all combine like in a ferromagnet and the motion aligns in these systems over billions of years towards optimization and the the dust from the fields interact with the objects in a way where the objects are either repelled, aligned or sucked into another system. I could be totally wrong, this is just my intuitive common sense talking. I would like to think that by using a comprehensive data gathering scheme combined with analysis that could show objects are actually connected by their actions like for instance a periodogram, I'd like to think that each galaxy is like the macro version of a large molecule and the quantum states of its atoms are the solar systems where each has either an up up, down, or an up up up, or some other combination of actually not so discreet contribution to the whole.