If the ability has in its cost, the value of X is copied.

The copy will have the same targets as the ability it's copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. If, for one of the targets, you can't choose a new legal target, then it remains unchanged (even if the current target is illegal).

An activated ability is written in the form "Cost: Effect."

If the ability is modal (that is, it says "Choose one —" or the like), the copy will have the same mode. You can't choose a different one.

If Illusionist's Bracers somehow becomes equipped to a creature an opponent controls, and an activated ability (that isn't a mana ability) of that creature is activated, you will control the copy of that ability.

If the cost of an activated ability requires Illusionist's Bracers or the equipped creature to be sacrificed, the ability won't be copied. At the time the ability is considered activated (after all costs are paid), Illusionist's Bracers is no longer equipped to that creature.

A mana ability is an ability that (1) isn't a loyalty ability, (2) doesn't target, and (3) could add mana when it resolves.