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Is it necessary to be based on the prefix, or can it be implemented by pattern, for instance, every even byte is zero, or the 4 bytes after the first 3 bytes must be all 7s, etc?

Is it simply brute-forcing hashes, looking for matching patterns that are not yet known?

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I don't see what prevents you from adding complexity.

And yeah, but it also requires valid transactions if you want to collect fees, as well as the knowledge of the valid previous block.

In practice Bitcoin treats SHA-256 outputs as integers, and requires them to be under a certain limit, based on the current difficulty.

That way we can make small adjustments to the difficulty. If we actually used a rule like "this many zeros in hex", the difficulty bumps would have to be rather large.

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