Can a battery powered by iron and air really provide a feasible power source for automobiles?
This is certainly possible.  In fact, there are a large number of metal-air batteries being developed all over the world.  

It is, however, strange that such high energy density is achieved, because iron ion itself would not offer very high energy density.  My guess is that likely they did it by having an extremely high matter density.  So this battery may be small in size for its capacity, but at the same time it may also be much heavier than a conventional battery. 

That could be why they brand it as a shuttle power supply(well, energy density isn't really relevant for a bus anyways).  A very heavy battery on a hand held device is never good.   Cost is the more important factor there, but it is hard to tell at the moment.  0 loss over 200 cycles seems like a fairy tale, but I will give them the benefit of the doubt at the moment.

This battery will also likely to have a considerable loss of charge when not in use.   Again, this might not be a huge problem for buses, where you keep driving non-stop during days then kept it in the charging station overnight.   

Anyways, don't expect this to be on your iPhone 10 or your laptop.  Even if it works as presented, it might not be that ideal for portable electronic devices, where people worry much more about weight and stand-by time than if it occasionally explodes, sadly.