On Falling Star, when you say deal 3 to a unit, does it remove the full 3 might, or just the HP part of the unit?

It just marks 3 damage — it doesn't touch the unit's Might at all.

In Riftbound, "dealing 3" puts 3 damage counters on the unit (Rule 417.1.b). Might and damage are tracked separately: a unit's Might stays at whatever its current modified value is, and damage just sits on it as a marker of how close it is to dying. The unit only actually dies during a Cleanup if its marked damage equals or exceeds its Might (Rules 142.4, 323.5).

So a 6-Might unit hit by one instance of Falling Star has 6 Might and 3 damage marked — it keeps all 6 Might. It won't die from that alone; you'd need to either deal 3 more damage or later reduce its Might below its marked damage (e.g., with a -Might effect). And note damage heals at end of turn or Combat Cleanup, so the "3 HP missing" state only persists until then.