What are the conditions for the timeframe of option in divorce, and does the delegation of divorce become void if the wife responds without the husband's knowledge or uses allusive phrases?

Intention is considered in delegating divorce. So, if the husband intended a specific duration, it would be according to what he intended.

If the husband delegates the divorce to his wife and she uses an ambiguous expression, her ruling in this regard is the same as the husband's. If the ambiguous expression is one that entails three divorces from the husband, then three divorces occur from the wife. If it is one of the subtle ambiguous expressions, then what she intended occurs.

The husband's knowledge of the wife's acceptance of the delegation is not required.