Does divorce take effect merely by intending it in the heart, and is the husband sinful for that, despite his provision of maintenance, and does he have other duties towards his wife and daughter during this period?

Divorce does not occur merely by intending it in the heart; rather, it requires verbal utterance and pronouncement. Scholars have adduced as proof for this the Prophet's (peace be upon him) saying: "Indeed, Allah has overlooked for my Ummah what they whisper to themselves, as long as they do not act upon it or speak of it." Thus, a mere intention of divorce or a promise of it does not bring about divorce. As long as you are providing for your wife and child, you are safe until the Sharia court rules between you.