Iron is always spoken of as the dividing line, but I'd like to know whether iron is exactly on the line, on one side (which?), or it depends. IOW, does fusion of iron atoms release energy (hydrogen side of the line), absorb energy (uranium side of the line), neither, or either (depending on conditions)?
That's because the periodic table is essentially about chemistry (i.e. about electron orbitals), not about nuclear physics (i.e. the atom's nucleus). For example it doesn't talk much about isotopes, aside from usually reporting the average atomic mass.
It will happily fuse further. It just won't support the outside of a star against gravity, while doing it. So the star collapses, fuses lots more stuff even heavier than iron, and then explodes. Most of the iron and heavier stuff fuses into the core of a neutron star, the ultimate in energy-consuming fusion.
Iron will not happily fuse further because this NEEDS energy and where would that energy come from?
"heavier than iron" elements are produced when a star explodes because that collapse produces enormous amounts of energy.
During the collapse, the outer edge of the star is accelerated to something like 20% of the speed of light, that is an ENORMOUS amount of energy slamming down on the core.
Lastly, neutron starts don't produce energy, they are the incompressible remnants of a dead star.
You answer your own question: the energy for further fusion, all the way to neutron degeneracy, is provided by gravitational collapse. The outer layers fusing provide energy for the explosion.
