It targets two monsters. Cards like Obelisk the Tormentor is fine with that, it cannot be targeted at all. Cards like Chaos Command Magician are not though, CCM can only protect itself from monster effects that choose one target. Penguin Soldier could bounce him, and another monster.
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There's a few issues here. - By Order of the Emperor can only be used against a monster effect that 'activates' when the monster is Normal Summoned. Obelisk has no effects that trigger from his own or any other monster's Normal Summon. His protective effects are all continuous, and BOotE cannot be used against his Ignition Effect. - Obelisk's summon cannot be responded to. So even if he did have a Trigger that could activate when he is summoned, BOotE could not chain its effect anyway. - By Order of the Emperor does not target the monster it is used against though. It is being used against the effect (you do not 'target' effects. Divine Wrath could be used against the activated effect of an untargetable monster). So to sum up, By Order of the Emperor cannot be used against Obelisk in any way. Cards like Divine Wrath can be used against Obelisk's Ignition Effect though, they do not target Obelisk.
The Equip happens on resolution of an Ignition Effect. Book of Moon can be chained to that. The target monster will flip face-down and then the Equip effect will resolve without effect because it can't equip to a Set monster. Inzektor Hornet will not move from whatever zone it started in.
SkyscraperField Spell/SPELLWhen a monster that includes "Elemental Hero" in its card name attacks, if its ATK is lower than the ATK of the attack target, increase the ATK of the attacking monster by 1000 points during damage calculation only.No, its effect does not activate. "When a monster...attacks...". This automatically tells you that it activates when your monster attacks, but does not activate if your monster is attacked.
It is ruled that Night Assailant cannot target itself when discarded, it can only target another Flip Effect monster.
To easily defeat Blue-Eyes Shining Dragon, use cards that don't target a specific monster on the field (Dark Hole, Mirror Force, Raigeki, etc.), since that monster's effect states that it can't be defeated by card effects that target this specific card.