Could this be a way to increase the transfer rate? Neurons can evolve with constant firing, they can even learn and store much more data. Is there a way to use them instead of electrical circuits?
No, not for the foreseeable future at least. We can't keep such cells active and stable outside the brain, let alone hooking them up to robotics.
On the upside, we do have neuromorphic computing already. People have designed hardware that behaves largely like neurons do, in order to optimize processing implementations. From Wikpedia:
"A key aspect of neuromorphic engineering is understanding how the morphology of individual neurons, circuits, applications, and overall architectures creates desirable computations, affects how information is represented, influences robustness to damage, incorporates learning and development, adapts to local change (plasticity), and facilitates evolutionary change."