The short answer is, if the player that activated Effect Veiler chooses, the monster's effect is negated if it activates during the End Phase. Here's what happens when you enter the End Phase. Imagine Player A activated Effect Veiler's effect on Player B's monster:
So if you control a Judgment Dragon that has its effect negated by Effect Veiler, your opponent can keep Judgment Dragon from sending cards off the top of your deck or let you.
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Forbidden Chalice will negate Marshamallon's 'cannot be destroyed by battle' effect. Because Forbidden Chalice changes the ATK of a monster, it can be used in the Damage Step, after Marshmallon is flipped by an attack. If you did this, you will not take the 1000 damage from Marshmallon either - his damage dealing effect activates after Damage Calculation, but will be negated.
Yes, generally you canBUT there are some cards that doesn't allow the effect to activate if you attack. Example is Chaos Sorcerer.so make sure to read the card text first.
Assuming the defending monster is also in attack position, both monsters will be destroyed.
Five-Headed Dragon.
Unless the monster specifically says otherwise, it takes two tributes for a monster of Lv7+