> What if the universe is anisotropic?

It is. Look up. Look down. The rock below and the sky above aren't homogeneous either (birds, clouds, trees; soil, roots, different size granules of sand and pebbles, clays, etc). But that's locally rather than at cosmologically-large scales.

Cosmic-scale isotropy and homgeneity give us a set of freefalling-in-deep-intergalaxy-cluster-space "Eulerian" observers who see, at the largest scales, a dust of galaxies surrounding them; we can build a set of coordinates that travel with these observers. These comoving coordinates are useful in cosmology, and are arguably "picked out" by the distribution of matter. From them we get the scale factor, a notion of cosmological time that applies throughout the entire universe. In principle any observer could determine a mapping between its preferred local system of coordinates and the comoving coordinates. In practice, we can determine the chemistry of distant objects via (red-shifted) spectral lines.

If the universe were anisotropic at the largest scales, but still homogeneous at the largest scales, we can consider a simple (dipole) case to start with: there is unignorably more matter and cosmic radiation in one half of the sky than in the other half, but each half has spiral galaxies galore. We would need a different system of cosmological coordinates, because observers to the left and right are effectively accelerated with respect to each other (and us, in the middle). The shape of the observable universe would differ; rather than the cosmic horizon(s) we have now that depend on the expansion history, we would have a set of Rindler-like wedges defining the boundaries of cause and effect that depend on both the expansion history and the relative anisotropy. Fascinatingly, the acceleration between the left and right gives an observer a very different evolution of particle numbers in each direction (if I remember late-noughties Einsteinian takes on Rastall's 1972 theory of gravitation, which I am not sure I do, the sparser half will fill with a surprisingly warm thermal bath, so the conservation of energy is broken much much harder in such a universe than in ours, which only has energy "disappear" as light and the like experience redshift with the expansion). We could of course complicate this into a multipole anisotropy, and get things that look even less like what we see. Because of that we "wash out" the local anisotropies (we ignore Andromeda and what we see of the Milky Way as "not cosmologically far enough") and find that the resulting isotropy and homogenity is a very good fit for the cosmic microwave background and ultra-deep-field astronomy. That will continue to be tested with gravitational wave astronomy.

Anisotropic and inhomogeneous cosmologies include those with supervoids and/or strangely-shaped masses (spirals and ellipticals here and there, but in other places or at supergalactic scales weirder structures dominate). One finds such cosmologies used in explorations of structure formation. These cosmologies can look much like ours, in terms of present-day observables. They're certainly more interesting for physicists when they are a very close match to our standard (homogeneous, isotropic) cosmology, but different enough to admit a different coupling between the expansion history and dark matter (the standard one dilutes dark matter in a predictable way at the largest scales, and similarly to the dilution of cold ordinary matter). Daniel Pomarède <https://en.wikipedia.org/wiki/Daniel_Pomar%C3%A8de> is a huge figure in that area of research, and the wiki bio is a good starting point if you have a deeper interest in your first question. Temperature winds up being very important, in part because of an acceleration between observers deep in a supervoid and observers in the non-void web-like or net-like structure, so we have to figure out why the cosmic microwave background doesn't seem to have large cold spots, and why the reticulated structure doesn't glow much warmer. This 2022 Starts With A Bang article by Ethan Siegal is relevant and may be of interest. <https://bigthink.com/starts-with-a-bang/cmb-cold-spot/>

Finally, your second and third questions are somewhere between "it's not necessary and doesn't really help" and "well if you adapt cosmology to favour a particular channel of early black hole formation you now need a mechanism to restore the small scale temperature fluctuations of the cosmic microwave background".