Does Herald of Kozilek reduce the cost of casting a face-down card? (With morph, etc)
Yes. It’s a colorless spell, so its cost is reduced by the Herald.

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Does Herald of Kozilek reduce the cost of casting a face-down card? (With morph, etc)
Yes. It’s a colorless spell, so its cost is reduced by the Herald.

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If I control an embodiment of fury/insight and cast atarka's command with the 3rd and 4th modes, do I get an elemental from the landfall trigger before the 4th mode resolves?
No.
You have to resolve Atarka’s Command fully before you can deal with any triggers that its resolution generates.