If akali moves to a BF and does 2 dmg. then leaves and does 2dmg. but it does not kill the unit. does the unit heal?

Yes — the unit heals, because a Combat Showdown was opened.

Since there was an enemy unit at that battlefield, Akali's arrival staged a Combat Showdown, and Combat Cleanup heals all Units in play regardless of whether the damage was lethal or whether the unit actually fought (Rule 466.1.a). Akali's "When I move" damage is just marked damage, not a kill — so it gets wiped at the end of that combat unless it killed the unit. Pulling her back with Rogue Assassin doesn't dodge this: the legend can only be activated at Action speed, meaning the Showdown is already running and will still clean up (FAQ #11658, #11899).

The one exception is if she's pulled out before the Showdown ever opens — i.e. moving her back at Reaction speed in response to her own move trigger while the chain is still non-empty (like a Flash), so no Combat was ever staged. In that case no Combat Cleanup occurs and the 4 damage stays marked (FAQ #11658). With the legend, that window doesn't exist.