golden apple

Effect
Activate only when you take Battle Damage while you control no monsters. Gain Life Points equal to the Battle Damage you took, and Special Summon 1 "Malus Token" (Fiend-Type/DARK/Level 1/ATK ?/DEF ?). Its ATK and DEF are each equal to the amount of Life Points you gained by this effect.

So....
1. When this card will activated? After we receive battle damage? (So if our LP is already 0, we can't activate this card?)
2. If opponent attack with Ancient Gear Golem or something that have similar effect, can we activate this card?

1. This card is activated during Damage Calculation, the point where the attacking monster's ATK is subtracted to your LP. After you take the damage you can activate this card. You lose the duel the moment your LP hits 0 so you cannot activate this card anymore.

2. Ancient Gear Golem prevents you from activating trap cards until the end of the Damage Step. The Golden Apples is activated DURING the Damage Step, specifically after recieving the battle damage, so you cannot use The Golden Apples when you receive a direct attack from Ancient Gear Golem.

that card is still activated in the damage step. To be exactly in substep 5, see Breakdown of the battle phase (should be at the same time as flashbang)