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approximately 4.5-5 billion years ago, a supernova event occurred in close proximity to the gas cloud our solar system would eventually coalesce from. Essentially, a massive star ran out of fuel (elements lighter than iron) in its core and could no longer generate radiation pressure in sufficient opposition to self gravity to maintain hydrostatic equilibrium. in the process of collapse, material falling into the core (at great speed) "bounces" of the super dense core, and under these extreme pressures fuses into the various elements heavier than iron, including gold.
These heavier elements are ejected from the supernova in relatively spherical shells that expand radially from the died star. As this material (in a vapor state) cools, it begins to condense. metals being the first to condense into a solid (including gold), then silicates around these metal cores and finally volatiles. At this point they are just football-shaped differentiated dust grains on the order of half a micron in size or so, and are moving far to quickly away from the supernova to really form anything, as they become more diffuse the further they spread out.
Now that gas cloud comes into play. the gas drags on the dust, slowing it down, while the dust, being just the right size, is able to cool the gas by blocking cosmic radiation (wavelength smaller than the dust grains), yet allowing thermal radiation to escape. Saying the gas cools is equivalent to saying the average kinetic energy of each gas molecule is decreased, and at some point the gas is moving slow enough that self gravity dominates over gas pressure, allowing nebular collapses into protoplanetary disks. Conserving the overall angular momentum of the gas cloud, dust and gas orbit around a common center of gravity, and through various collisional interactions circularize their orbits into a disk, at the center of which forms the proto-sun. heat from gravitational collapse, begins to vaporize the dust near the center of this disk, preferentially expelling volatiles, and allowing metal-silicate bodies to accrete (first through sticky collisions between particles, then static cling as complex particles become larger and polarized, and at some stage, gravity dominates. regardless, they start to clump together into large bodies.)
Eventually, planetary embryos are formed, and collide, forming the terrestrial planets we see today. heat from accretion and radioactive decay (more radioactive isotopes to fizzle so quickly after nova fusion) allow these bodies to gradually differentiate; that is to say that heavier (denser) material melts and sinks toward the center of gravity (why we have a dense metal core), and lighter materials rise to the surface. this process isn't perfect however, and heavier elements (like gold) can remain at any depth in the planet, albeit in small proportions as trace elements, general a few parts per billion.However, Earth is geologically active. surface and mantle rocks are continuously being melted and allowed to solidify. Liquid water flows on the surface an permeates the crust to great depths. minerals don't all melt at the same temperature, and rocks can have varying solubility in water depending on temperature and pressure. Processes such as fraction crystallization, can preferentially enrich magmas in trace elements, simply by crystallizing and removing major elements and minerals until these trace minerals are all thats left. If left to crystallize they can be brought to the surface by tectonic processes, or dissolved by geothermaly heated water and again be brought to the surface to precipitate out. where they can be mined as ore, dissolved in acid, and have they're precious content extracted, melted down, purified, molded, and surgically implanted into the mouths of people who probably ought to be investing in education rather than grills.
As for your second question, the IAU definition of a star requires that the body in question be fusing Hydrogen in its core, so no, the earth is not a star. however it is made from the debris from a star.