Can I use more than one reaction at a time?

Yes. You can use as many as you like.

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Does an effect like Disarm's prevent an attack from happening?
Disarms effect is
At the end of combat, return target Weapon to it's owner's hand unless they pay {r}.
So yes it does. If the weapon's owner doesn't pay 1, the weapon is removed immediatly and the original Action in the combat is effected by it, if itwas a weapon that weapon is no longer attacking, if it was an Action like Aggressive Assault, then it's base attack becomes 0

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