No, you cannot use Solemn Judgment to chain on Special Summons that are from activated effects (Mother Grizzly, Battle Fader, etc.). You can chain Solemn Judgment to cards that are Special Summoned through its own effect, while it does not have to be activated to do so (Cyber Dragon, Dark Armed Dragon, etc.).
Any effect that can negate Battle Fader's activation, will also state that it destroys the negated card. Battle Fader will go to the graveyard.
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.
No, it can't be used against Battle Fader at all in a battle situation.One confusing part of Yu-Gi-Oh is the distinction between summons that do not use the chain ('inherent' special summons is one term people use) and ones that summon themselves on resolution of their own activated effect.Examples of Inherent ones would be Synchro Summons, XYZ Summons and Chaos Sorcerer. Just like a Normal Summon, these do not use the chain. Solemn Judgment can be used against these, to negate the special summon.Many monsters can summon themselves with an activated effect. These are usually monsters in the graveyard (Plaguespreader Zombie) removed from play (DD Survivor) and any monster that summons itself as a response to a specific action (Gorz the Emissary of Darkness, Battle Fader). However most monsters are inherent-type.Next, consider what Solemn Judgment does. It can negate the activation of spell cards, and trap cards, and 'summons'. What it cannot negate is an activated monster effect, even if they special summon something on resolution. When you inherently special summon, there is a time when summon negation cards can be used. When you special summon by effect, the summon is complete, 'successful' when the effect resolves. That means you've got to chain to and negate the effect. If you allow the effect to resolve, there's no 'window' for a summon negating card.Because Solemn Judgment can't be used against activated monster effects, it can't be used at all against Gorz, Battle Fader, DD Survivor, Plaguespreader Zombie.On a side note. If Battle Fader's activation is negated, then its effect will not happen. That's because the summon and the battle phase ending part of the effect, is all one resolution. Stop that resolution, and no part of it happens. One card you could use is Solemn Warning, which can negate either a summon or an effect that would special summon, covering both kinds of special summon.
You use an effect that can negate the activation of a monster's effect. Divine Wrath is one. Solemn Warning is another - it can negate both inherent special summons, or effects that include special summons. Royal Oppression can stop Battle Fader, and it can stop Gorz if he's summoned outside the damage step by his 'direct damage' summon. But Royal Oppression can't be used in the damage step so it can't stop him when he's summoned from battle damage, but Counter Traps can.
Ride the Fader was created in 1996.
Fader Label was created in 2002.
Fernando Fader died in 1935.
Fernando Fader was born in 1882.
W. Fader has written: 'Qualifying procedures for health visitors'
Three Fact Fader was created on 2009-07-06.
Fader - Paradise Lost song - was created in 2001.
It ends the battle phase, so any current attack is unable to proceed (it would have caused a replay anyway). That's slightly different to 'negating' an attack, but the end result is the same.