Yes, Battle Fader's effect is a trigger, activated in hand when an opponent's monster declares an attack. Light and Darkness Dragon will chain to and negate this, meaning Battle Fader is not summoned and the battle phase does not end. Note that Light and Darkness Dragon does not destroy the cards it negates, so Battle Fader will remain in hand. It can be activated again when the next attack is declared.
Marshmallon has a Trigger Effect that deals damage and a continuous effect that prevents it from being destroyed by battle. If a face-down Marshmallon is attacked, it will first be flipped face-up. You will then calculate damage - unless LaDD's ATK has been reduced severely, more than likely no damage will be dealt. If LaDD's attack is higher, it doesn't matter as Marshmallon cannot be destroyed by battle. Marshmallon's effect will then trigger, Light and Darkness Dragon will chain to it and negate it, so no damage is dealt. Note that Light and Darkness Dragon does not destroy the cards he negates, so Marshmallon will remain on the field. Also note that Light and Darkness Dragon can do nothing to continuous effects as they do not 'activate'. That means he can do nothing against Marshmallon's battle protection.
Yes. Once Red-Eyes Darkness Metal Dragon is successfully summoned, there is a summon response window for cards like Bottomless Trap Hole. Only Spell Speed 2 or 3 effects can be used here. You can therefore use Fiendish Chain against it, which will resolve if not negated. That means that when Red-Eyes Darkness Metal Dragon is able to activate its Ignition Effect, it will be negated when it tries to resolve. However it is worth noting that you could always wait until Red-Eyes Darkness Metal Dragon tries to activate the effect, and chain Fiendish Chain to it, it will resolve first and therefore negate the dragon's effect too. So hitting it before it can activate is not actually necessary.
Yes. Most negation effects like Light and Darkness Dragon, and Stardust Dragon, can be used in the Damage Step, which is where Newdoria triggers. Stardust Dragon can indeed be used against Newdoria's activation.
No. The text has been changed but the effect remains the same, first it was a 'cannot be special summoned except by..' monster, which means only the listed method could ever be used, it was not the kind that could be brought back assuming you summoned it properly first. Now it says "Must be summoned by....cannot be summoned in any other way", again, it doesn't matter if you properly summoned it, it can't be summoned back from the graveyard.
Yes, Five-Headed Dragon only protects itself from being destroyed in battle against monsters with the specified Attributes.
In theory, yes. Light and Darkness Dragon's negation effect does not target, it could potentially be chained to Blue-Eyes Shining Dragon's Quick Effect. However becase Light and Darkness Dragon's effect is mandatory, in practice it will actually chain to the initial targeting effect, the one Blue-Eyes Shining Dragon was going to use its effect against.
Red-Eyes Darkness Metal Dragon's effect is an Ignition Effect so cannot be chained to anything.
Marshmallon has a Trigger Effect that deals damage and a continuous effect that prevents it from being destroyed by battle. If a face-down Marshmallon is attacked, it will first be flipped face-up. You will then calculate damage - unless LaDD's ATK has been reduced severely, more than likely no damage will be dealt. If LaDD's attack is higher, it doesn't matter as Marshmallon cannot be destroyed by battle. Marshmallon's effect will then trigger, Light and Darkness Dragon will chain to it and negate it, so no damage is dealt. Note that Light and Darkness Dragon does not destroy the cards he negates, so Marshmallon will remain on the field. Also note that Light and Darkness Dragon can do nothing to continuous effects as they do not 'activate'. That means he can do nothing against Marshmallon's battle protection.
You can only activate and Special Summon "Red Eyes Darkness Metal Dragon" with this effect from your hand.
If you special summon a Totem Dragon, and then tribute it for Red Eyes Darkness Metal Dragon, then Totem Dragon goes straight from field to the removed from play zone. It never hits the graveyard, and is therefore never a valid target for Red Eyes Darkness Metal Dragon's dragon summoning effect.
Yes, Stardust Dragon can activate its negation Quick Effect in the Battle Phase, and even the Damage Step.
Light and Darkness Dragon's first line of text says that it cannot be special summoned. Therefore when it is destroyed and its last effect triggers, it cannot choose itself.
No, Light and Darkness Dragon's negation effect is a Quick Effect which is spell speed 2, so it cannot chain to a Counter Trap which is spell speed 3.
Red-Eyes Darkness Metal Dragon's own summon does not use the chain. Because nothing is activating, there is nothing for Divine Wrath to chain to - Divine Wrath negates 'activations' of monster effects. Red-Eyes Darkness Metal Dragon's effect to special summon other dragons though is an Ignition Effect, which is a form of activated effect. This can be negated using Divine Wrath.
No, no card's effect can be activated while it is in deck.
a good strategy for light and darkness dragon is to include counter traps, because its effect cannot negate them. you could also try a beat down strategy where you negate your opponents card effects with light and darkness and attack for win.
Light and Darkness Dragon's effect can only be used once in any one chain. So if Enemy Controller was activated, Light and Darkness Dragon will automatically chain to this. If Book of Moon was added at Chain Link 3, then Light and Darkness Dragon can do nothing against it. Book of Moon will resolve, flipping LaDD face-down. Light and Darkness Dragon's effect can only resolve properly if on resolution it can lose 500 ATK and DEF, so its effect will fail to resolve if it has left the field or is face down. So Enemy Controller will resolve too (assume it targeted another monster).