What experiment would disprove Friedmann model of cosmology? What experiment would disprove Friedmann model of cosmology?
As a layman, I have read a lot of articles and threads in specialized forums. I am probably wrong, but I developed an impression that that theory is circular, 99.9% self- referential. The only hard experimental datum seems to be the redshift, and then most other parameters, distance, luminosity, age, scale factor, expansion rate, etc. are model-dependent and therefore confirm the theory, 
a) - what are the other hard facts at the bottom of the theory, if any?
If I am not wrong, the prerequisite of a scientific theory is that it can be disproved.
b) - how do you disprove that redshift is determined by stretching of space, 
c) - how do you disprove that space can expand and that just a metric devised by a theorist can make it expand?

spacetime is not an object expanding like some rubber foam. It's a combination of a manifold and metric. The expansion means the metric is time dependant, and this is explained by the requirement that the metric be a solution to Einstein's equation.

 A: The key output of the FLRW metric is the scale factor $a(t)$ as a function of time. From this we can calculate the time derivative $\dot{a}(t)$ (which is what the red shift measures) then check whether or not it satisfies the equation:
$$ \left(\frac{\dot{a}}{a}\right)^2 = \frac{8\pi G}{3} (\rho_{radiation} + \rho_{matter} + etc) $$
where the etc includes dark energy and anything else you may wish to throw in.
So basically the test is to measure the redshift as a function of distance. The problem is that this is extraordinarily hard to do on the scales where the matter distribution is homogeneous. There are various approaches being tried such as baryon acoustic oscillations and properties of galaxy clusters but it's still early days.
A: One simple test that directly probes the model is the consistency relation between the angular diameter distance $d_A(z)$ and the luminosity distance $d_L(z)$
$$d_L(z) = (1+z)^2 d_A(z)$$
This relation holds regardless of the content and state of the Universe. If this is found to be violated then it would be a hard blow against the Friedmann Universe as one can not just add new "stuff" to fix it.
This relation have been experimentally tested (will try to find the ref. when I get time, but if I rememeber correctly they parametrized $d_L(z) = (1+z)^{\beta} d_A(z)$ and fitted to data and found something like $\beta = 1.95 \pm 0.2$ [the numbers is from memory and should be taken with a grain of salt] perfectly consistent with the prediction.)
A: The Friedman model is derived from General relativity under the assumptions that on cosmological scales the Universe is homogeneous and isotropic. Therefor you could falsify the Friedman model by 


*
 
*Showing that on cosmological scales General Relativity is not a valid model (well it could happen)

* Showing that on cosmological scales the universe is not homogeneous. i.e. if you managed to show that significant density variations still existed on all length scales.

* Showing that on a cosmological scales the universe is not isotropic, i.e. showing that the distribution of matter in the universe has a preferred direction 


None of these seems terribly likely, but I don't think you were expecting a Physics SE post to show that most of Cosmology is invalid. 
A: On a plot of $\Omega_\Lambda$ versus $\Omega_M$, there are three sets of observations that provide constraints: supernovae, the cosmic microwave background, and baryon acoustic oscillations. These three regions in the $\Omega_\Lambda$-$\Omega_M$ plane all have a common region of intersection, which is quite small. If they had failed to overlap, it would have proved that there was a lack of consistency in cosmological models. If future improvements in the data reduce the sizes of these regions and they then fail to overlap, it will be the same problem.
At one time there were claims that the oldest globular clusters were older than the age of the universe inferred from Hubble expansion. If this had been correct, then it would have been evidence against Big Bang cosmology, or at least against a particular model. But in fact we're now living in the age of high-precision cosmology, and current data show that the clusters are younger than the universe after all.
Big Bang nucleosynthesis makes specific predictions about the relative abundances of various isotopes. In most cases, these predictions are correct, but there still seems to be a problem with the 7Li/H ratio. I don't think anyone is about to throw away all of modern cosmology over this issue, but at some point it needs to be resolved, or there's something wrong with either our cosmological models or our knowledge of nuclear physics.
It's possible according to GR for the universe to be rotating. Solar system observations allow us to put an upper limit on the rate of rotation. If the rate of rotation were proved to be nonzero, then it would violate the assumption of isotropy in Friedmann models. However, the observational constraints are already tight enough that they don't allow rotation to be a huge effect (e.g., centrifugal forces can't contribute significantly to cosmological expansion), so Friedmann models would still probably be good at least as approximations.
General relativity is not a self-consistent theory if energy-momentum is not locally conserved. Therefore any evidence of local nonconservation of energy-momentum would indicate that GR needed to be revised, and thus our cosmological models would also probably need to be revised. There is a history of people like Fred Hoyle seriously proposing that matter was spontaneously created in a vacuum (by something he called a "C field"). This hypothesis is testable, and there is currently no believable evidence for it.

How do you disprove that redshift is determined by stretching of space, how do you disprove that space can expand and that just a metric devised by a theorist can make it expand?

There have been serious proposals by Hoyle's supporters that redshifts were not purely cosmological but were at least partly "intrinsic." This would require some kind of unspecified modification to standard quantum mechanics, and there is no evidence to support such a modification. As explained in this article by Ned Wright, attempts to construct cosmological models using these ideas have not been successful; the resulting models are inconsistent with observation.
