is fiat then so is gold, because they both get value the same way: from the free market.
Fiat means "by decree, or order" which usually comes from a government. The U.S. dollar gets value because the government says it is legal tender to pay debt. That gives it automatic value without bothering to ask the free market.
Gold on the other hand doesn't get value because of what any government says. Same thing with Bitcoin.
As for who can mine, how to mine, control of the mining etc. That too is similar to gold. The answer is that anyone can do it, and nobody controls all of it. However, competition is now pretty fierce for Bitcoin mining, and it's usually done now by those interested in specializing. For average people it's easier to get bitcoins other ways, like working for them or buying them. I've personally never mined and found bitcoins, although I use them.
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