This hero card says: "Jonas' equipment cannot be destroyed. If Jonas reduces a monster to exactly 1 wound with an attack, it surrenders."
I assume, that means, that Jonas should reduce a monster to one life point, not to one wound. But that's not my question.
If Jonas attacks a monster with already only one lifepoint left but deals no damage, or if he reduces the life points of a monster by other means than attacking to 1 (for example by moving the monster into a pit), I assume, that his ability doesn't work?
Correct. It has to be an attack, and it has to be the attack that reduces the moster to 1 wound. An attack which does zero wounds on a monster with 1 wounds left does not 'reduce to' one wound.