The observable universe is statistically homogeneous and isotropic, although there are tensions with both the approximate homogeneity and the approximate isotropy. There are some interesting anomalies in the Planck observations of the CMB. The cosmic web is the clearly fractal and can only be viewed as homogeneous by gross coarse-grained analysis. The expansion is approximately uniform, as far as we know today. That may change.

The there is the fact that our local Hubble Bubble is probably not the entire Universe. It may be a small, or even infinitesimal part thereof.

These are very complicated issues and require following everything that is posted daily to arxiv.org.

Nothing about cosmology is set in concrete. We don’t know for sure what the dark matter is, there are accumulating problems with dark energy, and there is a growing recognition that the observable universe is not the Universe.