This effect can be activated at any point in the Damage Step, even "During Damage Calculation".
If you say "Damage Step?", and activate this effect, you have activated it at the Start of the Damage Step, not During Damage Calculation.
The effect of "Honest" is a Quick Effect.
The effect of "Honest" does not target the LIGHT monster.
Sending "Honest" to the GY is a cost to activate its effect.
The ATK increase is equal to the ATK of the opponent's monster when the effect of "Honest" resolves.
The ATK increases from the effects of multiple "Honest" are cumulative.
If you use the effect of "Honest" to increase the attack of "Asura Priest" or "Cyber-Twin Dragon", the ATK increase does not change when you battle a different monster.