What does an Einstein-De Sitter universe look like?
Bendiness = space-time curvature. 

And yes, it is flat (k=0) for the EdS model. Essentially it is the epoch at which only matter is thought to dominate (no contributions from radiative pressure or dark energy, $\Lambda$).

It is only a model. The EdS universe is thought of as a static Universe which is expanding indefinitely. It just makes solving certain equations in Cosmology a little easier, but it was perhaps due to Einstein's stubbornness in accepting a dynamic Universe.