What is the difference between an interpreter (mutāwil) and an ignorant person (jāhil)? And does one break an oath if they tied divorce to an action and then performed it ignorantly, or thinking that their action was not the one sworn upon, or not knowing that their action fell within the scope of what was sworn upon, especially given their extreme caution to avoid fulfilling the condition?

Ignorance is the lack of knowledge about something that one is supposed to know. As for the one who interprets, he is someone who understands a religious matter incorrectly, and this is a type of ignorance.

Regarding conditional divorce (ta'liq al-talaq): If a person makes a divorce conditional upon his own action, and then performs the action upon which the divorce was conditioned out of forgetfulness, ignorance, or compulsion, then the divorce does not occur. The same applies if he makes the divorce conditional upon the action of another, and that other person is aware of the condition. If that person then performs the action upon which the divorce was conditioned out of forgetfulness, ignorance, or compulsion, then the divorce does not occur. However, if the other person was not aware of the condition, then the divorce occurs, even with ignorance, forgetfulness, or compulsion.