What is the ruling on a vow that was to donate 5 pounds for every sin, then was expiated with money without fulfilling the conditions of expiation for an oath, then another vow was made to donate one pound for the same sin? And do the charities I have given with the intention of drawing closer to Allah suffice for the first vow, by analogy with someone who prays Duha with the intention of it being a Sunnah while forgetting that he had vowed it?

This vow is a vow of obstinacy and anger. What is obligatory regarding it is either fulfilling it or offering an expiation for an oath (kaffarat yameen). Since the previous expiation was not effective, you must either give five pounds in charity for each time you committed this act, or offer an expiation for each time. According to the Hanbalis, one expiation suffices for what has passed. Accordingly, you should offer one expiation, then resume your vow. If you do what you vowed to abandon, you should give six pounds in charity for both vows. If you do not adopt this opinion, you must count the expiations or offer what was vowed according to the number of times you committed this act, and if you are unaware of the number, then estimate it to the best of your ability. Voluntary charity does not suffice for an obligatory vow, nor does voluntary prayer for a vowed prayer, nor does voluntary fasting for a vowed fast. Rather, one's obligation is not discharged from a vow except with the intention of fulfilling it and specifying the vowed prayer.