Oh Jeez, not the multiverse again.
See the Wikipedia
shape of the universe article and note that two out of three options are
wrong.
The wikipedia article seems incomplete, in that there are actually four distinct homogeneous and isotropic spatial geometries, rather than three. But that's neither here nor there.
Something else that's wrong is the assumption that a flat universe must be infinite.
That's not an assumption. The FLRW model assumptions are that the the universe is homogeneous and globally isotropic.
If that's assumed,
then the only possible flat spatial geometry is that of the (infinite) Euclidean plane.
But it's obviously not valid to say that just because the observable universe is pretty close to homogeneous and isotropic, then then whole universe
must be so. Fortunately, pretty much nobody actually made such a claim--the FLRW family is an idealization to simplify things, not a literal truth. Its actual physical relevance is only that
the universe around us is close to a flat FLRW model; there is no suggestion that the universe arbitrarily far away must match the same FLRW model.
Notably, inflationary models of the Big Bang tend to explicitly break the assumptions of homogeneity and isotropy rather hard anyway.
There's no evidence for that whatsoever. Au contraire, the evidence supporting big-bang cosmology suggests a finite universe.
I agree with the first statement. I don't agree with the rest--the evidence is pretty agnostic on the shape of the universe on the scale much larger than the observable universe. Because it's not observable, an claim about it is going to be based on assumptions that there is no evidence for.
And whilst I'm on a roll, there is no evidence whatsoever to support the notion that the universe is somehow curved "in a higher dimension". Zip, zero, zilch. And as for PacMan world, pah.
I don't know what you're talking about here. I don't recall this ever coming up as a claim by anyone.