Does this harmonic balancer / crankshaft pulley look damaged?
To me it looks like the rubber between the inner and outer parts is at least cracked if not completely separated.
Yes, that's the rubber damper developing a crack on the crank pulley. It will need to be replaced.
As the name suggests, the primary purpose of the harmonic damper is to help counter torsional vibrations and resonance. A non-functional damper results in excessive wear and tear on the crankshaft bearings as there will be nothing to dissipate the energy generated by the engine's harmonics.
If this crack grows large enough, the outer part will be effectively free to spin independently of the crankshaft. Once this happens, all kinds of weird symptoms can crop up.
I know this thread is over a year old, but I had a similar experience some two years ago. It sounded like a slipping fan belt, but as I dont have a head that can extend to the point where I could see what was " slipping " I got a mechanic friend of mine to have a look and see. Sure enough the rubber inside the pulley had broken away and each time the engine was revved, you could see the rubber balancer moving out towards the radiator. Replaced the pulley and problem went away.