Why is pressure in a liquid the same in all directions? I'd like answers both in the more intuitive side an on the more precise side. 
Thinking of water as "cubes" of water, for example, would allow pressure in the z axis to be independent of the y or x axis. Choosing other "shapes", like a  triangular prism, yield different results. Will this fact, then, be dependent on the format of the molecules of the liquid ?
I've heard of the rotational symmetry of liquids. What is its precise statement ? Why is it true ?
 A: The pressure in three different directions is indeed independent for materials that are composed of cubes or other fixed shapes. But these materials are called solids, not liquids.
By definition, a liquid is a material without any regular crystallic or otherwise periodic structure. A liquid is composed of randomly arranged molecules that are as close to each other as the repulsive forces allow – the latter property distinguishes liquids from gases. Liquids and gases are two subgroups of a larger group called fluids.
When a milliliter of liquid is at rest, it means that in this milliliter of material, the molecules are randomly ordered and randomly moving so that their center-of-mass remains at rest. But when it's so, the only "force-related" quantity by which one milliliter of this liquid differs from another is the density or any function of it, such as the pressure. Because there's only one density, there's only one pressure.
Because liquids are not composed of fixed cubes but of chaotic molecules. a new molecule added to a volume of liquid with excessive pressure may escape in any direction. Whatever direction it chooses, the density (in molecules per unit volume) will be reduced to the appropriate value so the pressure may drop, too.
The independence of the fluids' pressure on the direction is known as Pascal's law and you may read an independent explanation at Wikipedia:

http://en.wikipedia.org/wiki/Pascal%27s_law

A: The answer easily follows from the definition of pressure itself. It is the force that the particles apply on the sides of the container per unit of distance. Particles do have dimensions, but for what concerns the calculations their dimensions are irrelevant when compared to the sides of the container (although little modifications can apply, if you use any other state equation rather than the law of perfect gases). If you assume that the particles randomly move, then there will be the same amount of particles (in average) hitting the unit side of the container in any direction, therefore the pressure will be the same on any side independent of what happens elsewhere.
A: 
Choosing other "shapes", like a triangular prism, yield different results.

Whatever, be the shape of the prism you chose, the result shall always be the same. Here is an example with a right-angled triangular prism of water (of infinitesimal volume, such that it is practically a point). Let's take the horizontal forces acting on the prism first.

$ F_c = F_bsin \theta$
$ P_cA_c = P_b A_bsin \theta$
$ P_cA_bsin\theta = P_b A_bsin \theta$
$P_c = P_b$
If you take the vertical forces, you will get $ P_a = P_b$; thus forces acting on the prism of water are of the same magnitude in all directions.
My explanation is built upon the fact that the net force acting on any imaginary plane inside a fluid is always is normal to it.
