Is a medium required between the cathode and anode? Must there be some kind of resistance? Cos i was thinking why dont you just grow the iron crystals then the nickel then the carbon nanotubes directly on top of each other? In one big 1m by 1m slabs what would the storage capacity be? Iron oxide is rust right? Nickel is used in margarine right? Carbon is ash? Graphene is pencils?

Wow, with few more tweaks, there could possibly be an application for Low Energy Nuclear Reaction (LENR) here as micro- or nano-Nickel, Hydrogen and graphene/CNT are the most promising ingredients for LENR...

Edison didn't invent the Nickle-Iron battery, Waldemar Jungner did! Edison only developed it further.

So, was there any increase in power density? Or is that what is referred to by "ultrafast" charge and discharge rates? I get the two confused: energy and power densities. Is there any comparison available (or given by the researchers) to show how these might be implemented compared to the various lithium-ion battery types? (Something similar to the comparison of the early types above where it would have taken twice the size and weight to match performance with lead-acid.) Does this solve most of the challenges of lithium-ion types? Is it manufacturable? Can the tech be commercialized, and if so, will it be less costly? How much development still must be done?
Great set-up (giving the history - very interesting), but the follow through on the current tech is a tad lacking...

as long as materials like carbon nanotubes and graphene are being used to improve this or other batteries, lithium ion batteries and internal combustion engines can sleep soundly.

Brian, thank you for a remarkable story from the past and an example of how J. D. Rockeller distrusted electric anything, we would be burning down the house if John had his way, and power was how he won. Now we have the power and John is dead. We need not burn anything save for bankers for our power, the sun and batteries like the Edison Nickle Iron will allow us to stop burning or drilling. Got sulfur?

So it charges and discharges fast, it is still heavy with low energy density.

Anyone can fast charge, discharge a tiny battery like the experiment here. In real life it's another story. Most batteries it's how it is constructed that controls how fast C/D happens.
Next NiFE is a water sucker needing watering every 5 cycles or so and produces a lot of H2/O2 gas. It self discharges rather fast and not eff charging are other deal breakers.
This is a losing line of attack and one would be better improving Li, molten salt, sulfur and other batteries that show so much more promise.
Fact is with a good EV design lead is a great, low cost battery that one can get 100 mile range from as some EV people do. My EV's use them that with a generator has unlimited range at over 100 mpg once the battery runs down which is rare.
Rather than new batteries we need lighter, stronger, more aero cars to put them in and you don't need expensive superbatteries.

As a Radio Technician apprentice in the late 1960's, my then boss found an old metal torch powered by a 2 cell nickle-iron battery in the back of a cupboard.
It was about 2.5" square and 6 - 7" high and had probably been sitting for 10 - 20 years and was covered in corrosion and completely dried out.
I was given the job of cleaning it, washing out the cells then making up the electrolyte solution from a powder my boss obtained from somewhere, filling and charging it. It went perfectly and in tests, had the capacity that was stamped on the case - Quite Amazing

As the article mentions (if you read it), it's a supplement for slow charging batteries based on lithium. Its designed power output and volume is not going to be dramatic in such a way that it negatively impacts the car's performance, but can actually improve it. It makes a lot of sense to use this material for regenerative braking, as the time frame for when you brake is relatively short compared to the time your batteries need to recharge.
The problem is not the energy density of this material. Mass producing graphene and nanocarbon tubes is still in its infancy and making these materials for everything except for research is inhibitive, because of its high cost. Going by the current state of affairs, you might want to think twice about having this technology in your car by that factor alone.