For example, Anticipate Peril gives a duration of "1 minute/level or until activated." Does that mean it lasts for a maximum of 1 minute per level but ends when activated? Or does it mean it lasts forever until activated and the 1 minute per level is superfluous?
The answer's in the description:
The first time during this spell's duration that the target has to make an initiative check, the creature adds an insight bonus on that initiative check equal to the spell's caster level (maximum +5). Once this bonus applies, the effects of the spell end.
The spell ends immediately after an initiative check (activation of the spell's effect). You must also make this initiative check before the duration ends, or the spell expires and has no effect.