When an effect does multiple things "on each board," can each thing happen in a different land?

When an effect does multiple things "on each board," can each thing happen in a different land?

Yes in principle, but most such effects specify otherwise.
By default, as long as you're resolving everything on a particular board, you can split the effect. For example, "On Each Board: Remove 1 Beasts. Add 1 Disease" (part of the first choice of the "Life's Balance Tilts" Event) can remove a Beasts token from one land and add a Disease token to a different land on the same board. And similarly, "On Each Board: Push up to 2 Dahan" (part of the first choice of the "Hard-Working Settlers" Event) can Push 2 Dahan from different lands on the same board.
Nevertheless, many of these effects specify that they happen in a single land on the board, which means that they can't be split. For example, if "On Each Board: Gather 1 or 2 Dahan into a land with Dahan Setup Symbols." (the "Return to Old Pillars" Dahan Event) moves two Dahan, it must move them into the same single land, since the Dahan are gathered into "a land" (singular).