Is what happened considered a valid khulʿ, taking into account the husband's intention behind his question "Did you validly initiate khulʿ?" and the wife's intention with "Yes" that she was requesting khulʿ?

If the spouses do not agree on a compensation for khulʿ (divorce at the wife's instance with compensation), then what happened is not considered khulʿ, because the preponderant opinion is that khulʿ is not valid without compensation. If it was with the word "divorce" or the intention of it, then it is a revocable divorce. If the husband did not intend to effect khulʿ, it does not occur even if they agreed on compensation. If it was in the form of a question, such as "Have you divorced yourself from me for a thousand dirhams?" and she said: "I have divorced myself," the scholars differed. Some of them said the contract is concluded, while others said it is not concluded until the husband accepts. Some detailed further, saying that if he intended to confirm it, it is concluded, but if he intended to bargain, it is not concluded, because the apparent meaning of an interrogative is bargaining.