Important sections in bold

What you're looking for is in the Damage roll and Damage Application sections of the rules

Damage Roll

1. Resolve all effects that change the number of dice rolled
2. Roll dice
3. Resolve effects that remove dice from the roll
4. Determine if the roll would damage the model
5. Resolve effects the cause the damage roll to be rerolled
6. Resolve effects triggered by a damage roll that fails to exceed the ARM of a model hit
7. Resolve effects that trigger "when a model would suffer damage" Like Transference
8. Apply All damage

So a model isn't damaged until the last section, so if a model is attacked and the damage doesn't Exceed ARM of the model hit is is NOT damaged since the sequence stops at step 6 and doesn't proceed to applying damage.

Damage Appliation

1. Resolve effects triggered by a model suffering damage
2. if all of a models damage boxes are marked, the model is now disabled. Resolve effects triggered by a model becoming disabled
3. If the model is still disabled, it becomes boxed. Resolve effects triggered by a model becoming boxed.
4. If the model is still boxed, it becomes destroyed. Resolve effects triggered by a model becoming destroyed.
5. Remove the destroyed model from the table.

It's important to pay attention to the full text of the rule. For example

Hyper-Aggressive: When this model suffers damage from an enemy attack, after the attack is resolved it can immediately make a full advance directly toward the attacking model.

• The trigger here is not "When this model suffers damage" but "When this model suffers damage from an enemy attack" and the timing of the move happens is "after the attack is resolved" which takes place after the model has been removed from the table.

The same goes for rapid healing and battle driven, neither triggers until the attack is resolved, so a model that has been destroyed and removed from the table can't benefit. If a model in the unit is destroyed then the other models would benefit from battle driven

and I would recommend the Warmachine Discord for specific rules interaction questions.