ATAR means that units will move across all tiles as if using the movement multiplier for roads (which you set in the .biq). So in the base game where roads triple the movement-rate, that means that a unit with M=1 will move up to 3 tiles per turn, M=2 will move up to 6 tiles, etc., even while in hostile territory. This can be extremely powerful, so use it sparingly!
Ignores movement cost for [Terrain] is more limited: that means that a unit will treat the specified Terrain as if it has a move-cost of 1, regardless of that Terrain's actual move-cost setting, e.g. (in the epic game) Hills and Forests cost 2 full movement points, so an M=2 unit which ignores Hills or Forests can travel up to 2 tiles per turn through those terrains, instead of stopping on the first tile. It should be noted that this unit-setting (1) is really only useful when the unit itself has M>1, and (2) only affects movement, not Worker-job times, which are multiplied by the Terrain's movement cost (e.g. using a single Worker, Mining cost-2 Hills will take twice as long as Mining cost-1 Grassland).
Regarding bombard-capable units, the 'Bombard' unit-action is what allows the human player to use that unit's B.R.F values, when the range-value (R) is >0, to make a stand-off attack on a nearby tile/unit (i.e. with no risk of dying).
With R=0, when part of a stack, the unit will bombard defensively, using its bombard-strength-value (B) against an attacking unit's A-value, removing up to 1 HP from the attacker -- or, if it has the ability, do Collateral Damage to buildings when it attacks a garrisoned town -- regardless of whether it has the Bombard-ability.
) that Flag is broken.
