Any player can play this in response to any tool card being played. The tool card then no longer works.
When Negate is used against a tool card with multiple targets, it only cancels the effect for one specific target.
Negate can be used both during and outside a player's turn. It can counter any tool card regardless of who played it or who the target is.
A player can use Negate on their own tool cards.
Negate can be used to counter another Negate. A second Negate can counter the first, and a third can counter the second, continuing this chain indefinitely.
To negate a delay tool card, Negate must be used at the time of judgment, not when the delay card is placed.