Is iron oxide magnetic in nanoparticle size? Because if it is, then we can probably very efficiently filter it before releasing it into the atmosphere.
Even if it isn't we are very good at filtering materials from exhaust gasses. Something like a wet electrostatic precipitator is probably overkill, but would do the job without having to care about magnetic properties.
Traditional methods or their combination: wet scrubber, electrostatic precipitator or bag filters will do the job.
iron oxide magnetic properties depend on its oxidation state, temperature and particle size.
Not sure why this is dead, but AFAIK magnetism in iron and steel is dependent on "domains" of iron molecules that are aligned in a crystal structure so the magnetic effect isn't just scattered to all directions. That's why some kinds of stainless steel aren't magnetic - the adulturant elements break up the crystal structure. In this case I think the question would be whether these particles are big enough to form a "domain" and become magnetic.
If the output is iron oxide, no it is only very very weakly magnetic.
And if iron(III) oxide is near the melting point, it's unlikely to be magnetic and may not even be paramagnetic. This would be an interesting lab experiment: heat a sample to 1500 C exactly and test for paramagnetic properties.
at nanoscale many (all?) iron oxides become super-paramagnetic. If anything, they're even more attracted to magnetic fields.
The article mentions a HEPA filter.
That’s still a mess, if the particles are magnetic a magnet will be a way cleaner and more effective filter.
Unfortunately, you're mistaken. In practice, iron(iii) oxide is barely paramagnetic and the particles are likely well above the Curie point and possibly at the melting point.