According to the TNG tech manual, the smooth curves of the ship makes it easier to maintain a warp field in a shape that uses less power while traveling at warp. So, not aerodynamic, but voidynamic, or something.

Iirc borg have transwarp as well as backup warp capability. And as to “how it works”: I was under the impression that, regardless of the type of warp reactor (federation dilithium/antimatter, Romulan microsingularity, whatever the borg use, etc) the main important output is a shitload of energy, and the thing generating the energy is largely irrelevant - all that matters is that an Alcubierre effect is generated, and serves as superluminal motive force.