The mesh chops up the air into smaller pieces and otherwise acts as an impeller to work the centrifugal part of the pump like an impeller. An impeller, with large flat blades, performs better with a homogeneous liquid. But a needlewheel/meshwheel is designed to work better with a two-phase mixture because it mixes as it pushes.
It can be round, and often is. The most important thing is that the wheel is balanced... like a ceiling fan. I suppose there is no reason why a suare, octagon, or perhaps a star shape wouldnt work.