Are planets and stars things on the same "spectrum"?

As noted above, an iron core fusing isn’t just a matter of pressure. You are trying to slam together nuclei that will only deign to do so if you add the energy deficit inherent in the mass change of the resultant nucleus. This is, as a good approximation, not dissimilar to all of the energy released when you took the lighter elements and fused them to get the iron in the first place. Or, is exactly the same energy released when you fission the new heavy elements back to iron. We are talking energies similar to the sum of the entire energy released by the star over many many millions of years, all concentrated into a tiny moment in time as the core of the supernova collapses in a freefall. The energy is utterly insane. Indeed “insane” doesn’t seem to be even on the same planet as the word needed to describe the energy.

White dwarfs are, in fact, largely iron. And neutron stars, of course, are mostly not made up of any chemical element at all, and what elements they do contain (in their outer layers) are mostly isotopes which would be impossible under less extreme conditions.

To fuse even deuterium (which is significantly easier than ordinary hydrogen) requires 13 times the mass of Jupiter (this is usually used, nowadays, as the cutoff for the definition of a “brown dwarf”). Since there are fewer than 13 outer planets, and since Jupiter is the largest of them, it follows trivially that all of the outer planets combined would not be enough even for the simplest form of fusion.

According to wikipedia, white dwarfs are usually oxygen and carbon, Depending on the initial mass of the star you might get neon and magnesium or a low mass star that can’t fuse helium could become a helium white dwarf.

As far as I know, our sun is never going to make iron.