Does divorce occur in the two aforementioned cases: first, when mistaking "la" (لا - no/not) and "illa" (إلا - except) in a negative formulation; and second, when the husband says, "You are not my wife? Then you are not my wife, so tell that to the judge," without intending divorce, and does obsessive doubt affect the ruling?

The questioner's obsessive thoughts have worsened due to indulging them and not striving against the self to abandon them. The best cure for this, after seeking Allah's help, is to disregard them. Regarding the question, if the husband genuinely uttered the first word of divorce, then at most, it would be a slip of the tongue, and divorce does not occur unless there is an intention to pronounce it. As for the second instance, his statement, "You are not my wife," is among the ambiguous expressions of divorce (kinayat) by which divorce does not occur unless there is an intention. Since he did not intend divorce, it does not occur.