Plutonium can not be mined on earth because it has all decayed due to its relatively short half-life compared to the age of the solar system.
Um, Pu-238 has a relatively short half-life (87.7 years) but some varients of plutonium, like Pu-244, have a half-life of 80 million years meaning it can be found in nature in trace amounts.
Pu is created as waste product in most nuclear reactors, and can then be separated relatively easy (chemistry). In contrast separating U-235 from U-238 is extremely complicated because both are identical to chemistry, so physics is needed, usually by exploiting the slightly different atomic weight.
No, it cannot. By weight, Pu-238 only makes up between 1-2% of spent nuclear fuel. It is also combined with all the other by products of nuclear fission which compose of varying levels of elements from zinc and up. Spent nuclear fuel is a hodgepodge of elements and very radioactive/dangerous.
Separating U-235 from U-238 is simple, but expensive, using centrifuges. The heavier U-238 ends up on the outside of the centrifuge and the lighter U-235 ends up on the inside. This is why so many countries have been able to get significant enough quantities of U-235 to do something with it--it just takes money and a little ingenuity.
Producing Pu was the main reason why the US built nuclear reactors during WW2.
Hanford B Reactor created Pu-239 that was used in the "Trinty" atomic test and "Fat Man" atomic bomb. It created Pu-239 by bombarding U-238 with neutrons.
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