The literal shape of space became a topic with Einstein's theory of general relativity. Before that, there had certainly been arguments about whether space was unbounded or had some limit, but they were mostly philosophical. In general relativity space-time is a mathematical manifold whose geometry is linked to observable features such as gravity, the ...
Whereof we cannot speak, thereof we must remain silent.
Boundaries in space are not a major topic. As far as we can tell there are none.
Boundaries in time are real. There is a pretty big boundary 13.7 billion years ago: the big bang. It is as far as we can tell a singularity: no physical theory can describe the conditions at the instant of the big bang, ...
The BBC article pointed out by @uhoh in a comment answers the question nicely.
To work out how old the grains were, the researchers measured how long
they had been exposed to cosmic rays in space. These rays are
high-energy particles that travel through our galaxy and penetrate
Some of these rays interact with the matter they ...
Yes, a "flat" universe is infinitely large, and hence "non-circular". I think perhaps you are confusing a flat and "closed" geometry.
A flat universe is a universe where your good old high-school math works as expected: the angles of a triangle sum up to $\pi$ radians (180 degrees), the circumference of a circle is $\pi$ times its diameter, ...
There are no such theories because there is an immediate problem with both scenarios as stated.
It is a fact that a spherical shell of material has no net gravitational influence on material anywhere inside it. https://en.wikipedia.org/wiki/Shell_theorem