If I understand your question correctly, the homogeneity at large scales ( a few Gly) is perfectly consistent with the linear + small perturbation evolution of the fluctuations measured via the CMB at the time of decoupling

It's a very interesting question, as there are rather few ways to probe the interior of the past light cone at the same cosmic time, to do a real test. We are currently using the fossil record of galaxies at different distances to probe their past world lines, and this allows us to test to what extent the average star formation rate is homogeneous. This is not a full test, of course - to do that would require demonstration that the metric was Friedmann-Robertson-Walker, and that has not been done. We should have some results soon. As Steve says, observations of the CMB and large scale structure are consistent with homogeneity (give or take fluctuations) but strictly they are on the past light cone, so are more a test of isotropy.

The spatial homogeneity can only be observed if we go back in time to the early

universe, almost immediately after the big bang. In earlier times to 400,000 years,

where matter and radiation were still coupled.

see also Scrimgeour et al. 2012 which uses galaxy clustering... however, such an analysis will always rely on the FRW metric...

All observations / experiments in physics reside in the backward light cone. The difference in cosmological observations is that as very large length scales are involved we become aware of this. Take the example of any observation related to quantum mechanical length scales where we take special relativity into account (more precisely speaking many particle quantum mechanics incorporating special relativity i.e. quantum field theory).

Actually the "event" (observation) is in the past light cone but because the length scales are small the "signal" (mainly particles like the photon) carrying the result of "observation" seems to reach our detectors instantly and we are under the illusion that we are observing the "present".

It dependent on the model. for example in Stephanim model see our paper

2004CQGra..21.3953G (http://arxiv.org/abs/astro-ph/0403534)

In string landscape theory, our universe is not FRW but has a bubble topology with a center etc. I would like to know what one can say from observations without assuming a FRW metric and without assuming the "cosmological principle" which proposes that the universe would look the same to observers in other galaxies.

The CMB has a bearing mostly on isotropy and only indirectly on matter homogeneity. I would like to know what are the limits on a systematic dependence of matter density on distance as opposed to fluctuations. To see where I am coming from see ArXiv:1205.3138 .

I agree with Leandros. The only reliable way, at the moment, to test matter homogeneity is CMB.

But, Salvatore, the CMB tells us only that matter was isotropic relative to us at a given point in time (decoupling time) and at the corresponding distance from us. It says little, I believe, about the matter density as a function of position. Non e vero? Galaxy counts and cluster counts could say something but again, I would not like to assume a FRW metric or that the universe looks the same to observers everywhere.

I understand your point. So the only way-out could be to take into account a suitable cosmological volume where there is a reasonable transition to homogeneity and isotropy. Someone estimated such volume which should be of the order of (100-120 Mpc)^3. In this case,

To L.Clavelli:Some of questions you are interested in are discussed in: http://arxiv.org/abs/1206.5993.