Do all units heal after a non-combat showdown (unit gets rebuked or FoFd and no combat damage is assigned)?

No, units do not heal after a non-combat showdown.

According to RiftJudge FAQ #7792 and #3513, healing only occurs after combat showdowns and at the end of the turn. Non-combat showdowns do not trigger this healing process.

Even if combat damage is skipped or units are removed from the battlefield (e.g., via effects like "rebuke" or "FoFd") after a combat showdown has been initiated, the units will still heal because the combat showdown itself occurred. However, if the showdown is non-combat (uncontested), no such healing trigger exists.