Nobody knows what the topology of the universe is, nor, contrary to this animation, does anyone have a reliable estimate for the size of the universe (as opposed to just the observable universe). It might be infinite, or it might be just slightly larger than the observable universe.
But yes, all current models of the universe are homogeneous; no point is more central than any other point. It doesn't have to be this way, but it's the simplest assumption.
"Yes and no". The universe is not homogeneous on a large scale, there are filaments of galaxies and everything but yes the idea of the center of the universe does not correspond to anything. The Big Bang from current models happened everywhere and the expansions comes from the fact that the very "fabric" of the universe expands.
But there are some awesome implications of an infinite universe, take a look here if you are interested:
In the sense of matter distribution, the universe isn't homogeneous on small scales either. But that's not what is meant in the context of a cosmological model. The global spacetime is modeled with a FLRW metric, whose key property is homogeneity and isotropy.
But yes, all current models of the universe are homogeneous; no point is more central than any other point. It doesn't have to be this way, but it's the simplest assumption.