Is there a simple way to state the hypotheses of the Big Bang theory? I have the impression that the Big Bang singularity is merely a consequence of Freedman equations. Could somebody clarify what belongs to the Big Bang theory and what is a consequence of Freedman equations?
If you "run the clock backwards" using the Friedmann equations, you can avoid a singularity; you just need the pressure and energy to behave in the right way when the Universe was very hot and dense. The catch is that "the right way" in this case means that $\rho + 3 p < 0$; in other words, either the energy density or the pressure (or both) have to be negative. No conventional forms of matter are known that satisfy this inequality, so unless something really strange was going on in the early Universe, there must have been an initial singularity. (Or, more plausibly, there was a time in the early Universe where the spacetime curvature was sufficiently large that the laws of GR as we know them did not apply.)
This result, by the way, is one of the Penrose-Hawking singularity theorems, which are a series of quite general results developed by Hawking and Penrose in the late '60s and early '70s. They basically say that if gravity gets strong enough, matter isn't doing anything too weird, and the causal structure of the universe is sufficiently predictable, then you'll get a singularity. (The precise meanings of "strong enough", "too weird", and "sufficiently predictable" vary from theorem to theorem.) If you want to read more about these theorems, check out the first lecture in this series.
The way I would put it, then, is that the Big Bang Singularity (or something like it) is a natural consequence of the Friedmann equations and the behavior of standard sources of matter and energy.
The Big Bang was originally just the zero time limit of the FLRW metric. I'm not sure that Big Bang Theory has a meaning outside of CBS, but to the extent that it does have a meaning it is synonymous with the solution to Einstein's equations for a homogenous isotropic universe.
Life is more complicated now because we believe the universe underwent a period of inflationary expansion. These days we tend to use the phrase Big Bang to mean the point at which inflation stopped and normal expansion took over, though I think some still take it to mean the time zero limit.
The Big Bang theory is just that a "theory". If it were true the universe would be a thin layer on the surface of an expanding sphere like a balloon being inflated. That is the only way you can have the appearance of galaxies moving away from each other with equal velocity. A telescope pointed in any direction in space observes galaxies in all observable directions. The observations don't match what we would expect to observe. Galaxies on one spherical plane and nothing perpendicular to it. Can no one else see this?