When an effect happens "on each board," can it be split among multiple lands on that board?

When an effect happens "on each board," can it be split among multiple lands on that board?

Yes, unless the effect affects "a land" / "a single land" or is otherwise more specific.
To illustrate the difference, "On Each Board: Push 2 Dahan from a land with Blight to a land without Blight" ("Forsake the Barren Land") must Push both Dahan from the same land because they must both leave "a land with Blight." In contrast, "On Each Board: Push up to 2 Dahan" ("Hard-Working Settlers") can simultaneously Push Dahan from different lands, since it doesn't set any conditions on which land(s) the Dahan leave.
Similarly, if such an action has multiple instructions, like "On Each Board: Add 1 Beasts. Remove 1 Disease." ("Life's Balance Tilts"), it can resolve each of its instructions in a different land (in this case, adding a Beasts token in one land and removing a Disease token from a different land).