Chemistry - Is iron the most stable element in the periodic table?

Solution 1:

Yes, $^{56}\ce{Fe}$ has the most stable nucleus, and $\ce{He}$ is the most chemically inert element. These are different and unrelated qualities, pretty much like physical fitness and intelligence in a man. As for structural stability, there is no such thing in chemistry (there is one in architecture and another in mathematics, but those are out of scope of this question).

Solution 2:

No, nickel-62 is the most stable on a binding energy per nucleon basis. Fe-58 is second and Fe-56 is third.

See Fewell, M. P., "The Atomic Nuclide with the Highest Mean Binding Energy", Am. J. Phys., vol. 63, pages 653-658.